{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume678","volumeNumber":8021,"name":"Dagstuhl Seminar Proceedings, Volume 8021","dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume678"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article2000","name":"08021 Abstracts Collection \u2013 Numerical Validation in Current Hardware Architectures","abstract":"From 06.01. to 11.01.2008, the Dagstuhl Seminar 08021 ``Numerical Validation in Current Hardware Architectures'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.\r\nDuring the seminar, several participants presented their current\r\nresearch, and ongoing work and open problems were discussed. Abstracts of\r\nthe presentations given during the seminar as well as abstracts of\r\nseminar results and ideas are put together in this paper. The first section\r\ndescribes the seminar topics and goals in general.\r\nLinks to extended abstracts or full papers are provided, if available.","keywords":["Computer arithmetic","arbitrary precision","floating-point arithmetic standardization","language support","reliable libraries,high-precision special functions","reliablealgorithms","reliable floating-point and interval computing on different platforms"],"author":[{"@type":"Person","name":"Luther, Wolfram","givenName":"Wolfram","familyName":"Luther"},{"@type":"Person","name":"Cuyt, Annie","givenName":"Annie","familyName":"Cuyt"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Markstein, Peter","givenName":"Peter","familyName":"Markstein"}],"position":1,"pageStart":1,"pageEnd":31,"dateCreated":"2008-04-23","datePublished":"2008-04-23","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Luther, Wolfram","givenName":"Wolfram","familyName":"Luther"},{"@type":"Person","name":"Cuyt, Annie","givenName":"Annie","familyName":"Cuyt"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Markstein, Peter","givenName":"Peter","familyName":"Markstein"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2001","name":"08021 Summary \u2013 Numerical Validation in Current Hardware Architectures","abstract":"Numerical validation in current hardware architectures - From embedded system to high-end computational grids \r\n\r\nTopics\r\nList of participants\r\nSchedule\r\nList of talks","keywords":["Computer arithmetic","arbitrary precision","floating-point arithmetic standardization","language support","reliable libraries","high-precision special functions","reliablealgorithms","reliable floating-point and interval computing on different platforms"],"author":[{"@type":"Person","name":"Cuyt, Annie","givenName":"Annie","familyName":"Cuyt"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Luther, Wolfram","givenName":"Wolfram","familyName":"Luther"},{"@type":"Person","name":"Markstein, Peter","givenName":"Peter","familyName":"Markstein"}],"position":2,"pageStart":1,"pageEnd":0,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Cuyt, Annie","givenName":"Annie","familyName":"Cuyt"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Luther, Wolfram","givenName":"Wolfram","familyName":"Luther"},{"@type":"Person","name":"Markstein, Peter","givenName":"Peter","familyName":"Markstein"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2002","name":"A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range","abstract":"A so called staggered precision arithmetic is a special kind of\r\n a multiple precision arithmetic based on the underlying \r\n floating point data format (typically IEEE double format) \r\n and fast floating point operations as well as exact dot product computations.\r\n Due to floating point limitations it is not an arbitrary precision arithmetic.\r\n However, it typically allows computations using several hundred mantissa digits. \r\n\r\n A set of new modified staggered arithmetics for real and \r\n complex data as well as for real interval and\r\n complex interval data with very wide exponent range is presented. \r\n Some applications show\r\n the increased accuracy of computed results compared to ordinary staggered\r\n interval computations. The very wide exponent range of the new arithmetic\r\n operations allows computations far beyond the IEEE data formats. \r\n\r\n The new arithmetics would be extremly fast, if an exact dot product was\r\n available in hardware (the fused accumulate and add instruction is only \r\n one step in this direction).","keywords":["Staggered correction","multiple precision","C-XSC","interval computation","wide exponent range","reliable numerical computations","complex interval funct"],"author":[{"@type":"Person","name":"Blomquist, Frithjof","givenName":"Frithjof","familyName":"Blomquist"},{"@type":"Person","name":"Hofschuster, Werner","givenName":"Werner","familyName":"Hofschuster"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"}],"position":3,"pageStart":1,"pageEnd":23,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Blomquist, Frithjof","givenName":"Frithjof","familyName":"Blomquist"},{"@type":"Person","name":"Hofschuster, Werner","givenName":"Werner","familyName":"Hofschuster"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2003","name":"A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC","abstract":"C-XSC is a powerful C++ class library which simplifies the development\r\nof selfverifying numerical software. But C-XSC is not only a development tool, it also provides a lot of predefined highly accurate routines to compute reliable bounds for the solution to standard numerical problems.\r\n\r\nIn this note we discuss the usage of a reliable linear system solver to compute the solution of problem 7 of the SIAM 100-digit challenge. To get the result we have to solve a 20 000 \u00c3\u0192\u00e2\u20ac\u201d 20 000 system of linear equations using interval computations. To perform this task we run our software on the advanced Linux cluster engine ALiCEnext located at the University of Wuppertal and on the high performance computer HP XC6000 at the computing center of the University of Karlsruhe.\r\n\r\nThe main purpose of this note is to demonstrate the power\/weakness of our approach to solve linear interval systems with a large dense system matrix using C-XSC and to get feedback from other research groups all over the world concerned with the topic described. We are very much interested to see comparisons concerning different methods\/algorithms, timings, memory consumptions, and different hardware\/software\r\nenvironments. It should be easy to adapt our main routine (see Section 3 below) to other programming languages, and different computing environments. Changing just one variable allows the generation of arbitrary large system matrices making it easy to do sound (reproducible and comparable) timings and to check for the largest possible system size that can be handled successfully by a specific package\/environment.","keywords":["C-XSC","reliable computing","100-digit challenge","reliable linear system solver","high performance computing","large dense linear systems"],"author":[{"@type":"Person","name":"Kolberg, Mariana","givenName":"Mariana","familyName":"Kolberg"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Zimmer, Michael","givenName":"Michael","familyName":"Zimmer"}],"position":4,"pageStart":1,"pageEnd":14,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kolberg, Mariana","givenName":"Mariana","familyName":"Kolberg"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Zimmer, Michael","givenName":"Michael","familyName":"Zimmer"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2004","name":"A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling","abstract":"Techniques of reliable computing like interval arithmetic can be used to\r\nguarantee a reliable solution even in the presence of numerical round-off\r\nerrors. The need to trace bounds for the error function separately can be \r\neliminated using these techniques. In this talk, we focus on some \r\ndemonstrations how the techniques and algorithms of reliable computing \r\ncan be applied to the construction and further processing of hierarchical \r\nsolid representations using the octree model as an example.\r\n\r\nAn octree is a common hierarchical data structure to represent 3D \r\ngeometrical objects in solid modeling systems or to reconstruct a real \r\nscene. The solid representation is based on recursive cell decompositions \r\nof the space. Unfortunately, the data structure may require a large amount \r\nof memory when it uses a set of very small cubic nodes to approximate a \r\nsolid.\r\n\r\nIn this talk, we present a novel generalization of the octree model created \r\nfrom a CSG object that uses interval arithmetic and allows us to extend the \r\ntests for classifying points in space as inside, on the boundary or outside \r\nthe object to handle whole sections of the space at once. Tree nodes with \r\nadditional information about relevant parts of the CSG object are \r\nintroduced in order to reduce the depth of the required subdivision. \r\nFurthermore, this talk is concerned with interval-based algorithms for \r\nreliable proximity queries between the extended octrees and with further \r\nprocessing of the structure. We conclude the talk with some examples of \r\nimplementations.","keywords":["Reliable solid modeling","hierarchical data structure"],"author":{"@type":"Person","name":"Dyllong, Eva","givenName":"Eva","familyName":"Dyllong"},"position":5,"pageStart":1,"pageEnd":4,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Dyllong, Eva","givenName":"Eva","familyName":"Dyllong"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2005","name":"A Software Library for Reliable Online-Arithmetic with Rational Numbers","abstract":"An overview of a novel calculation framework for scientific computing in integrable spaces is introduced. This paper discusses some\r\nimplementation issues adopted for a software library devoted to exact rational\r\nonline-arithmetic operators for periodic rational operands codified in fractional positional notation.","keywords":["Computable analysis","online-arithmetic","rational numbers"],"author":[{"@type":"Person","name":"de Miguel Casado, Gregorio","givenName":"Gregorio","familyName":"de Miguel Casado"},{"@type":"Person","name":"Garc\u00eda Chamizo, Juan Manuel","givenName":"Juan Manuel","familyName":"Garc\u00eda Chamizo"}],"position":6,"pageStart":1,"pageEnd":3,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"de Miguel Casado, Gregorio","givenName":"Gregorio","familyName":"de Miguel Casado"},{"@type":"Person","name":"Garc\u00eda Chamizo, Juan Manuel","givenName":"Juan Manuel","familyName":"Garc\u00eda Chamizo"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2006","name":"C-XSC and Closely Related Software Packages","abstract":"C-XSC and Closely Related Software Packages","keywords":["Mathematical software","reliable computing","C-XSC","CoStLy","ACETAF"],"author":[{"@type":"Person","name":"Hofschuster, Werner","givenName":"Werner","familyName":"Hofschuster"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Neher, Markus","givenName":"Markus","familyName":"Neher"}],"position":7,"pageStart":1,"pageEnd":4,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Hofschuster, Werner","givenName":"Werner","familyName":"Hofschuster"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"},{"@type":"Person","name":"Neher, Markus","givenName":"Markus","familyName":"Neher"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.7","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2007","name":"Complete Interval Arithmetic and its Implementation","abstract":"A Complete Interval Arithmetic and its Implementation is discussed.","keywords":["Interval Arithmetic","implementation"],"author":{"@type":"Person","name":"Kulisch, Ulrich","givenName":"Ulrich","familyName":"Kulisch"},"position":8,"pageStart":1,"pageEnd":12,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Kulisch, Ulrich","givenName":"Ulrich","familyName":"Kulisch"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.8","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2008","name":"Distributed parameter and state estimation in a network of sensors","abstract":"In this paper, we have considered distributed bounded-error state estimation applied to the problem of source tracking with a network of wireless sensors. Estimation is performed in a distributed context, emph{i.e.}, each sensor has only a limited amount of measurements available. A guaranteed set estimator is put at work. At each time instant, any sensor of the node has its own set estimate of the location of the source.","keywords":["Parameter estimation","state estimation","bounded errors","nonlinear estimation"],"author":{"@type":"Person","name":"Kieffer, Michel","givenName":"Michel","familyName":"Kieffer"},"position":9,"pageStart":1,"pageEnd":14,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Kieffer, Michel","givenName":"Michel","familyName":"Kieffer"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.9","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2009","name":"Extending the Range of C-XSC: Some Tools and Applications for the use in Parallel and other Environments","abstract":"There is a broad range of packages and libraries for verified numerical\r\ncomputation. C-XSC is a library combining one of the most extensive\r\nsets of functions and operations on the one hand with a wide range of\r\napplications and special features on the other hand. As such it is an\r\nimportant task both to make use of its existing capabilities in applications\r\nand to develop further extensions giving access to additional areas and\r\nenvironments.\r\nIn this talk, we present some examples of extensions for C-XSC that\r\nhave been developed lately. Among these are extensions that give access\r\nto further hardware and software environments as well as applications\r\nmaking use of these possibilities.\r\nSoftware libraries for interval computation always imply great computation\r\neffort: One way to reduce computation times is the development\r\nof parallel methods to make use of parallel hardware. For this, it is important\r\nthat the features and data types of the used library can be easily\r\nused in parallel programs. An MPI package for C-XSC data types allows\r\nto easily use C-XSC in parallel programs without bothering about the internal\r\nstructure of data types. Another extension of C-XSC, the C-XSC\r\nTaylor arithmetic, is also covered by the MPI package. Parallel verified\r\nlinear system solvers based on the package are available as well, and further\r\ndevelopment has been and is being done to integrate more efficient\r\nmethods for interval linear system solution.\r\nOne application making use of the mentioned extensions is a parallel\r\nverified Fredholm integral equation solver. Some results are given to\r\ndemonstrate the reduction of computation time and, at the same time,\r\nthe accuracy gain that can be obtained using the increased computation\r\npower. Naturally, hardware interval support would offer still more\r\npossibilities towards optimal performance of verified numerical software.\r\nAnother possibility to extend the range of C-XSC is to make results\r\navailable for further computations in other software environments as,\r\nfor example, computer algebra packages. An example of this is presented\r\nfor the Maple interval package intpakX. This kind of interfaces also\r\nallows the user to get access to further platforms like operating systems,\r\ncompilers or even hardware.\r\n\r\nReferences:\r\n[1] ALiCEnext: http:\/\/www.alicenext.uni-wuppertal.de.\r\n[2] Blomquist, F.; Hofschuster, W.; Kraemer, W.: Real and Complex Taylor\r\nArithmetic in C-XSC. Preprint BUW-WRSWT 2005\/4, University of\r\nWuppertal, 2005.\r\n[3] Grimmer, M.; Kraemer, W.: An MPI Extension for Verified Numerical Computations\r\nin Parallel Environments. In: Int. Conf. on Scientific Computing\r\n(CSC\u201907, Worldcomp\u201907) Las Vegas, June 25-28, 2007, Proceedings\r\npp. 111-117, Arabnia et al. (eds.), 2007.\r\n[4] Grimmer, M.: An MPI Extension for the Use of C-XSC in Parallel Environments.\r\nPreprint BUW-WRSWT 2005\/3, University of Wuppertal,\r\n2005.\r\n[5] Grimmer, M.: Selbstverifizierende mathematische Softwarewerkzeuge im\r\nHigh Performance Computing. Dissertation, Logos Verlag, Berlin, 2007.\r\n[6] Grimmer, M.: Interval Arithmetic in Maple with intpakX. In: PAMM -\r\nProceedings in Applied Mathematics and Mechanics, Vol. 2, Nr. 1, p.\r\n442-443, Wiley-InterScience, 2003.\r\n[7] Hofschuster, W.; Kraemer, W.: C-XSC 2.0: A C++ Library for Extended\r\nScientific Computing. Numerical Software with Result Verification, Lecture\r\nNotes in Computer Science, Volume 2991\/2004, Springer-Verlag, Heidelberg,\r\npp. 15 - 35, 2004.\r\n[8] Klein, W.: Enclosure Methods for Linear and Nonlinear Systems of Fredholm\r\nIntegral Equations of the Second Kind. In: Adams, Kulisch: Scientific\r\nComputing with Result Verification, Academic Press, 1993.","keywords":["C-XSC","Integral Equations","Interval Arithmetic","Maple","MPI","Parallel Environment","Taylor Arithmetic","Verified Linear System Solver."],"author":{"@type":"Person","name":"Grimmer, Markus","givenName":"Markus","familyName":"Grimmer"},"position":10,"pageStart":1,"pageEnd":14,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Grimmer, Markus","givenName":"Markus","familyName":"Grimmer"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.10","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2010","name":"Fast (Parallel) Dense Linear Interval Systems Solvers in C-XSC Using Error Free Transformations and BLAS","abstract":"The traditional solver for linear interval systems available in C-XSC [6,1]\r\nis mathematically based on the Krawczyk[12] operator and modifications\r\nintroduced by Rump[17]. The Krawczyk operator is composed of\r\nmatrix\/vector operations. These operations are realized in C-XSC\r\nwith higest accuracy (only one final rounding) using a so called long \r\naccumulator (dotprecision variable). C-XSC dotprecision variables allow the \r\nerror free computation of sums of floating point numbers as well as the \r\nerror free computation of scalar products of floating point vectors. Thus, \r\nfrom a mathematical point of view these operations are perfect. Because \r\nactual hardware does not support these perfect scalar products all \r\noperations have to be realized by software. This fact leads to a tremendous \r\ntime penalty (note: it has been shown that with modest additional hardware \r\ncosts perfect scalar products can be made as fast as simple floating-point \r\nloops). \r\n\r\nTo speed up the C-XSC scalar product software-operations we adapt the so \r\ncalled DotK algorithm as published in [14]. Error free transformations[14,3,4,10]\r\nare used as basic building blocks to develop summation and scalar product \r\nalgorithms simulating a K-fold precision. Compared to the perfect C-XSC operations \r\nthese operations are fast. They are more accurate than simple floating-point\r\nloops (but of course no longer perfect in the mathematical sense). The fast \r\noperations are available in C-XSC via the new data types DotK, IDotK, CDotk\r\nand CIDotK. These new data types are composed in such a way that traditional \r\nC-XSC code using dotprecision variables can be adapted with minimal effort. It is \r\npossible to switch (at runtime!) from perfect computations to fast operations using \r\nK-fold precision (K equal 0 means traditional dotprecision computations) and it is \r\npossible to hold intermediate results with corresponding error bounds for further\r\nsummations or scalar product updates. The details are described in [19].\r\n\r\nAdditionaly, based on similar algorithms used in Intlab[16], BLAS and LAPACK \r\nlibraries [2] are used in the O(n\u00c3\u201a\u00c2\u00b3) parts of the linear system solver. For\r\nmatrix-matrix products, manipulation of the rounding mode of the processor is used \r\nto compute enclosures of the correct result.\r\n\r\nComparing the traditional solver with the new version shows that the class of \r\nproblems which are solvable with the new version is smaller than the class of \r\nproblems which can be solved using the solver based on perfect operations. But it \r\nseems that for real world problems also the new solver is appropriate. Using the \r\nnew solver based on BLAS and simulating a quadrupel precision (i.e. k==2) the \r\nspeedup comes close to 200(!). The new solver is nearly as fast as the corresponding \r\nIntLab[16] solver verifylss. Solving a real linaer system of dimension 1000 on a \r\nPentium 4 with 3.2GHz takes about 2.8 seconds. In all cases tested the accuracy of \r\nour new solver was better and in some cases significantly better than the accuracy \r\nof the corresponding IntLab results. The new solver also allows solving larger \r\n(dense) problems than its IntLab counterpart. We also show some examples where IntLab \r\nfalls down whereas our new solver still works.\r\n\r\nA parallel version of this solver, based on ScaLAPACK, is also available. Unlike\r\nthe previous parallel solver in C-XSC[5], this new solver does not depend on a \r\nroot-node, which makes it possible to compute a verified solution even of very large \r\nlinear systems.\r\n\r\nIn the talk we will discuss the new data types in more detail, we will emphasize our\r\n modifications to the DotK algorithm taken from the literature [14,15], we will show \r\ntime measurements and we will present results concerning the accuracy of the computed\r\nenclosures. Our results will also be compared to corresponding results computed with \r\nthe IntLab package. We also will comment on hardware features and compiler options\r\nwhich can\/should be used to get reliable results on different platforms efficiently.\r\n\r\n\r\nReferences:\r\n\r\n[1] Downloads: \r\nC-XSC library: http:\/\/www.math.uni-wuppertal.de\/~xsc\/xsc\/cxsc.html\r\nSolvers: http:\/\/www.math.uni-wuppertal.de\/~xsc\/xsc\/cxsc_software.html\r\n\r\n[2] L.S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, \r\nL. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, R. C. Whaley, An Updated Set \r\nof Basic Linear Algebra Subprograms (BLAS), ACM Trans. Math. Soft., 28-2 (2002), pp. 135--151.\r\n\r\n[3] Bohlender, G.; Walter, W.; Kornerup, P.; Matula,\r\nD.W.; Kornerup, P.; Matula, D.W.:\r\nSemantics for Exact Floating Point Operations.\r\nProceedings, 10th IEEE Symposium on Computer Arithmetic,\r\n 26-28 June 1991, IEEE, 1991.\r\n\r\n[4] Dekker, T.J.: A floating-point technique for extending\r\nthe available precision. Numer. Math., 18:224, 1971.\r\n\r\n[5] Grimmer, M.: Selbstverifizierende Mathematische Softwarewerkzeuge im\r\nHigh-Performance Computing. Konzeption, Entwicklung und Analyse am Beispiel\r\nder parallelen verifizierten Loesung linearer Fredholmscher Integralgleichungen\r\nzweiter Art. Logos Verlag, 2007.\r\n\r\n[6] Hofschuster, W.; Kraemer, W.:\r\nC-XSC 2.0: A C++ Library for Extended Scientific Computing.\r\nNumerical Software with Result Verification,\r\nLecture Notes in Computer Science, Volume 2991\/2004,\r\nSpringer-Verlag, Heidelberg, pp. 15 - 35, 2004.\r\n\r\n[7] Kersten, Tim: Verifizierende rechnerinvariante Numerikmodule, Dissertation,\r\nUniversity of Karlsruhe, 1998\r\n\r\n[8] Klatte, Kulisch, Wiethoff, Lawo, Rauch:\r\n\"C-XSC - A C++ Class Library for Extended Scientific Computing\",\r\nSpringer-Verlag, Heidelberg, 1993.\r\nDue to the C++ standardization (1998) and dramatic changes\r\nin C++ compilers over the last years this documentation describes\r\nno longer the actual C-XSC environment. Please refer to more accurate\r\ndocumentation (e.g.[1]) available from the web site of our\r\nresearch group: http...\r\n \r\n[9] Kirchner, R., Kulisch, U.:\r\nHardware Support for Interval Arithmetic.\r\nReliable Computing, Volume 12, Number 3,\r\nJune 2006 , pp. 225-237(13).\r\n\r\n[10] Knuth, D.E.: The Art of Computer Programming: Seminumerical Algorithms.\r\nAddison Wesley, 1969, vol. 2.\r\n\r\n[11] Kulisch, U.: Computer Arithmetic and Validity - Theory,\r\nImplementation. To appear.\r\n\r\n[12] Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, \r\nComputing, 4:187-201, 1969.\r\n\r\n[13] Lerch, M.; Tischler, G.; Wolff von Gudenberg, J.; Hofschuster, W;\r\nKraemer, W.:\r\nfilib++, a Fast Interval Library Supporting Containment Computations.\r\nACM TOMS, volume 32, number 2, pp. 299-324, 2006.\r\n\r\n[14] Ogita, T., Rump, S.M., Oishi, S.: Accurate sum and\r\ndot product. SIAM Journal on Scientific Computing,\r\n26:6, 2005.\r\n\r\n[15] Oishi, S., Tanabe, K., Ogita, T., Rump, S.M., Yamanaka, N.:\r\nA Parallel Algorithm of Accurate Dot Product.\r\nSubmitted for publication, 2007.\r\n\r\n[16] Rump, S.M.: Intlab - Interval Laboratory. Developments in Reliable\r\nComputing, pp. 77-104, 1999.\r\n\r\n[17] Rump, S.M.: Kleine Fehlerschranken bei Matrixproblemen, Dissertation, \r\nUniversity of Karlsruhe, 1980\r\n\r\n[18] Stroustrup, Bjarne: The C++-Programming Language, 3rd Edition, Addison-Wesley, 2000.\r\n\r\n[19] Zimmer, Michael: Laufzeiteffiziente, parallele Loeser fuer\r\nlineare Intervallgleichungssysteme in C-XSC, Master thesis,\r\nUniversity of Wuppertal, 2007.\r\n\r\n\r\nAMS subject classification: 65H10, 15-04, 65G99, 65G10, 65-04","keywords":["Error-free transformations","K-fold accuracy","accurate dot product","C-XSC","high accuracy","dense linear systems","verified computation."],"author":[{"@type":"Person","name":"Zimmer, Michael","givenName":"Michael","familyName":"Zimmer"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"}],"position":11,"pageStart":1,"pageEnd":20,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Zimmer, Michael","givenName":"Michael","familyName":"Zimmer"},{"@type":"Person","name":"Kr\u00e4mer, Walter","givenName":"Walter","familyName":"Kr\u00e4mer"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.11","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2011","name":"Implementation of the reciprocal square root in MPFR","abstract":"We describe the implementation of the reciprocal square root --- also called\r\ninverse square root --- as a native function\r\nin the MPFR library. The difficulty is to implement\r\nNewton's iteration for the reciprocal square root on top's of GNU MP's\r\n\textsc{mpn} layer, while guaranteeing a rigorous $1\/2$ ulp bound on the\r\nroundoff error.","keywords":["Multiple precision","floating-point","inverse square root","correct rounding","MPFR library"],"author":{"@type":"Person","name":"Zimmermann, Paul","givenName":"Paul","familyName":"Zimmermann"},"position":12,"pageStart":1,"pageEnd":3,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Zimmermann, Paul","givenName":"Paul","familyName":"Zimmermann"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.12","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2012","name":"Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation","abstract":"A parallel version of the self-verified method for solving linear systems\r\nwas presented on PARA and VECPAR conferences in 2006. In this research we propose improvements aiming\r\nat a better performance. The idea is to implement an algorithm that uses technologies\r\nas MPI communication primitives associated to libraries as LAPACK,\r\nBLAS and C-XSC, aiming to provide both self-verification and speed-up at the\r\nsame time. The algorithms should find an enclosure even for very ill-conditioned\r\nproblems. In this scenario, a parallel version of a self-verified solver for dense\r\nlinear systems appears to be essential in order to solve bigger problems. Moreover,\r\nthe major goal of this research is to provide a free, fast, reliable and accurate\r\nsolver for dense linear systems.","keywords":["Linear systems","result verification","parallel computing"],"author":[{"@type":"Person","name":"Kolberg, Mariana","givenName":"Mariana","familyName":"Kolberg"},{"@type":"Person","name":"Bohlender, Gerd","givenName":"Gerd","familyName":"Bohlender"},{"@type":"Person","name":"Claudio, Dalcidio","givenName":"Dalcidio","familyName":"Claudio"}],"position":13,"pageStart":1,"pageEnd":5,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kolberg, Mariana","givenName":"Mariana","familyName":"Kolberg"},{"@type":"Person","name":"Bohlender, Gerd","givenName":"Gerd","familyName":"Bohlender"},{"@type":"Person","name":"Claudio, Dalcidio","givenName":"Dalcidio","familyName":"Claudio"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.13","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2013","name":"Interval Arithmetic and Standardization","abstract":"Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds.\r\nOperations for intervals can be efficiently implemented. There is an unanimous agreement, how to define the basic operations,\r\nif we exclude division by an interval containing zero. Hence, it should be standardized.\r\nFor division by zero, two options are possible, the clean exception free interval arithmetic or the containment arithmetic. \r\nThey can be standardized as options.\r\nElementary functions for intervals can be defined. In some application areas loose evaluation of functions, \r\ni.e. evaluation over an interval which is not completely contained in the function domain, is recommended, \r\nIn this case, however, a discontinuity flag has to be set to inform that Brouwer's fixed point theorem is no longer applicable in that case.","keywords":["Intervals","containment sets","IEEE754r"],"author":{"@type":"Person","name":"Wolff von Gudenberg, J\u00fcrgen","givenName":"J\u00fcrgen","familyName":"Wolff von Gudenberg"},"position":14,"pageStart":1,"pageEnd":14,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Wolff von Gudenberg, J\u00fcrgen","givenName":"J\u00fcrgen","familyName":"Wolff von Gudenberg"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.14","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2014","name":"Numerical Verification Assessment in Computational Biomechanics","abstract":"In this paper, we present several aspects of the recent project PROREOP, in which a new prognosis system is developed for optimizing patient-specific preoperative surgical planning for the human skeletal system. We address verification and validation assessment in PROREOP with special emphasis on numerical accuracy and performance. To assess numerical accuracy, we propose to employ graded instruments, including accuracy tests and error analysis. The use of such instruments is exemplified for the process of accurate femur reconstruction. Moreover, we show how to verify the simulation results and take into account measurement uncertainties for a part of this process using tools and techniques developed in the project TellHIM&S.","keywords":["Numerical verification assessment","validation","uncertainty","result verification"],"author":[{"@type":"Person","name":"Auer, Ekaterina","givenName":"Ekaterina","familyName":"Auer"},{"@type":"Person","name":"Luther, Wolfram","givenName":"Wolfram","familyName":"Luther"}],"position":15,"pageStart":1,"pageEnd":15,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Auer, Ekaterina","givenName":"Ekaterina","familyName":"Auer"},{"@type":"Person","name":"Luther, Wolfram","givenName":"Wolfram","familyName":"Luther"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.15","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2015","name":"On the Interoperability between Interval Software","abstract":"The increased appreciation of interval analysis as a powerful tool for controlling round-off errors and modelling \r\nwith uncertain data leads to a growing number of diverse interval software. Beside in some other aspects, \r\nthe available interval software differs with respect to the environment in which it operates and the provided \r\nfunctionality. Some specific software tools are built on the top of other more general interval software but \r\nthere is no single environment supporting all (or most) of the available interval methods. On another side, \r\nmost recent interval applications require a combination of diverse methods. It is difficult for the end-users \r\nto combine and manage the diversity of interval software tools, packages, and research codes, even the latter \r\nbeing accessible. Two recent initiatives: [1], directed toward developing of a comprehensive full-featured library \r\nof validated routines, and [3] intending to provide a general service framework for validated computing in \r\nheterogeneous environment, reflect the realized necessity for an integration of the available methods and \r\nsoftware tools.\r\n\r\nIt is commonly understood that quality comprehensive libraries are not compiled by a single person or small \r\ngroup of people over a short time [1]. Therefore, in this work we present an alternative approach based on \r\ninterval software interoperability.\r\n\r\nWhile the simplest form of interoperability is the exchange of data files, we will focus on the ability to run \r\na particular routine executable in one environment from within another software environment, and vice-versa, \r\nvia communication protocols. We discuss the motivation, advantages and some problems that may appear in \r\nproviding interoperability between the existing interval software.\r\n\r\nSince the general-purpose environments for scientific\/technical computing like Matlab, Mathematica, Maple, etc. \r\nhave several features not attributable to the compiled languages from one side and on another side most problem \r\nsolving tools are developed in some compiled language for efficiency reasons, it is interesting to study \r\nthe possibilities for interoperability between these two kinds of interval supporting environments. \r\nMore specifically, we base our presentation on the interoperability between Mathematica [5] and external \r\nC-XSC programs [2] via MathLink communication protocol [4]. First, we discuss the portability and reliability \r\nof interval arithmetic in Mathematica. Then, we present MathLink technology for building external \r\nMathLink-compatible programs. On the example of a C-XSC function for solving parametric linear systems, \r\ncalled from within a Mathematica session, we demonstrate some advantages of interval software interoperability. \r\nNamely, expanded functionality for both environments, exchanging data without using intermediate files and \r\nwithout any conversion but under dynamics and interactivity in the communication, symbolic manipulation interfaces \r\nfor the compiled language software that often make access to the external functionality from within Mathematica \r\nmore convenient even than from its own native environment. Once established, MathLink connection to external \r\ninterval libraries or problem-solving software opens up an array on new possibilities for the latter.\r\n\r\nReferences:\r\n\r\n[1] G. Corliss, R. B. Kearfott, N. Nedialkov, S. Smith: Towards an Interval Subroutine Library, \r\nWorkshop on Reliable Engineering Computing, Svannah, Georgia, USA, Feb. 22-24, 2006.\r\n\r\n[2] W. Hofschuster: C-XSC: Highlights and new developments. In: Numerical Validation in Current Hardware \r\nArchitectures. Number 08021 Dagstuhl Seminar, Internationales Begegnungs- und Forschungszentrum f\"ur \r\nInformatik, Schloss Dagstuhl, Germany, 2008.\r\n\r\n[3] W. Luther, W. Kramer: Accurate Grid Computing, 12th GAMM-IMACS Int. Symposium on Scientific Computing, \r\nComputer Arithmetic and Validated Numerics (SCAN 2006), Duisburg, Sept. 26-29, 2006.\r\n\r\n[4] Ch. Miyaji, P. Abbot eds.: Mathlink: Network Programming with Mathematica, Cambridge Univ. Press, Cambridge, 2001.\r\n\r\n[5] Wolfram Research Inc.: Mathematica, Version 5.2, Champaign, IL, 2005.","keywords":["Software interoperability","interfacing","interval software","C-XSC","MathLink","Mathematica"],"author":{"@type":"Person","name":"Popova, Evgenija D.","givenName":"Evgenija D.","familyName":"Popova"},"position":16,"pageStart":1,"pageEnd":13,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Popova, Evgenija D.","givenName":"Evgenija D.","familyName":"Popova"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.16","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2016","name":"Robustness of Boolean operations on subdivision-surface models","abstract":"This work was presented in two parts at Dagstuhl seminar 08021.\r\n The two presentations described work in\r\nprogress, including a ``backward bound'' for a combined backward\/forward\r\nerror analysis for the problem mentioned in the title.\r\n\r\nWe seek rigorous proofs that representations of computed sets, produced by\r\nalgorithms to compute Boolean operations, are well formed, and that the\r\nalgorithms are correct. Such proofs should eventually take account of the use of\r\nfinite-precision arithmetic, although the proofs presented here do not.\r\n\r\nThe representations studied are based on subdivision surfaces. Such\r\nrepresentations are being used more and more frequently in place of trimmed\r\nNURBS representations, and the robustness analysis for these new representations\r\nis simpler than for trimmed NURBS.\r\n\r\nThe particular subdivision-surface representation used is based on the Loop\r\nsubdivision scheme. The analysis is broken into three parts. First, it is\r\nestablished that the input operands are well-formed two-dimensional manifolds\r\nwithout boundary. This can be done with existing methods.\r\nSecondly, we introduce the so-called ``limit mesh'', and view the\r\nlimit meshes corresponding to the input sets as defining an approximate problem\r\nin the sense of a backward error analysis. The presentations mentioned above\r\ndescribed a proof of the corresponding error bound. The third part of the\r\nanalysis corresponds to the ``forward bound'': this remains to be done.","keywords":["Robustness","finite-precision arithmetic","Boolean operations","subdivision surfaces"],"author":[{"@type":"Person","name":"Jiang, Di","givenName":"Di","familyName":"Jiang"},{"@type":"Person","name":"Stewart, Neil","givenName":"Neil","familyName":"Stewart"}],"position":17,"pageStart":1,"pageEnd":10,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Jiang, Di","givenName":"Di","familyName":"Jiang"},{"@type":"Person","name":"Stewart, Neil","givenName":"Neil","familyName":"Stewart"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.17","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2017","name":"Second Note on Basic Interval Arithmetic for IEEE754R","abstract":"The IFIP Working Group 2.5 on Numerical Software (IFIPWG2.5) wrote on 5th Septem- \r\nber 2007 to the IEEE Standards Committee concerned with revising the IEEE Floating- \r\nPoint Arithmetic Standards 754 and 854 (IEEE754R), expressing the unanimous \r\nrequest of IFIPWG2.5 that the following requirement be included in the future computer \r\narithmetic standard: \r\n\r\n For the data format double precision, interval arithmetic should be made \r\n available at the speed of simple floating-point arithmetic. \r\n\r\nIEEE754R (we believe) welcomed this development. They had before them a document \r\ndefining interval arithmetic operations but, to be the basis of a standards document, it \r\nneeded more detail. Members of the Interval Subroutine Library (ISL) team were asked \r\nto comment, in an email from Ulrich Kulisch that enclosed one from Jim Demmel to Van \r\nSnyder raising the issue. This paper provides ISL's comments.","keywords":["Interval arithmetic","validated computation","floating point","standards","exceptions","not an interval"],"author":[{"@type":"Person","name":"Pryce, John D.","givenName":"John D.","familyName":"Pryce"},{"@type":"Person","name":"Corliss, George C.","givenName":"George C.","familyName":"Corliss"},{"@type":"Person","name":"Kearfott, R. Baker","givenName":"R. Baker","familyName":"Kearfott"},{"@type":"Person","name":"Nedialkov, Ned S.","givenName":"Ned S.","familyName":"Nedialkov"},{"@type":"Person","name":"Smith, Spencer","givenName":"Spencer","familyName":"Smith"}],"position":18,"pageStart":1,"pageEnd":8,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Pryce, John D.","givenName":"John D.","familyName":"Pryce"},{"@type":"Person","name":"Corliss, George C.","givenName":"George C.","familyName":"Corliss"},{"@type":"Person","name":"Kearfott, R. Baker","givenName":"R. Baker","familyName":"Kearfott"},{"@type":"Person","name":"Nedialkov, Ned S.","givenName":"Ned S.","familyName":"Nedialkov"},{"@type":"Person","name":"Smith, Spencer","givenName":"Spencer","familyName":"Smith"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.18","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2018","name":"The CoStLy C++ Class Library","abstract":"CoStLy (ul{Co}mplex ul{St}andard Functions ul{L}ibrarul{y}) has been\r\ndeveloped as a C++ class library for the validated computation of function\r\nvalues and of ranges of complex standard functions. If performed in exact arithmetic, the inclusion functions for principal branches compute\r\noptimal range bounds. For the sake of accuracy, a major effort has been made in the implementation of the algorithms in floating point arithmetic to eliminate all intermediate expressions subject to numerical overflow, underflow, or cancellation. The CoStLy library has been extensively tested for arguments with absolute values ranging from 1.0E-300 to 1.0E+300. For most arguments, the computed bounds for function values are highly accurate. In many test cases, the observed precision of the result was about 50 correct bits (out of the 53 bits available in IEEE 754 floating point arithmetic) for point arguments.","keywords":["Complex interval arithmetic","inclusion functions"],"author":{"@type":"Person","name":"Neher, Markus","givenName":"Markus","familyName":"Neher"},"position":19,"pageStart":1,"pageEnd":6,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Neher, Markus","givenName":"Markus","familyName":"Neher"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.19","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2019","name":"The New IEEE-754 Standard for Floating Point Arithmetic","abstract":"The current IEEE-754 floating point standard\r\nwas adopted 23 years ago. IEEE chartered a committee to \r\nrevise the standard to include new common practice in \r\nfloating point arithmetic, to incorporate decimal floating \r\npoint into the standard, and to address the issue of \r\nreproducible results. This talk will visit these issues, \r\nbased on the current work of the IEEE-754 revisions \r\ncommittee, which expects that a new standard will be \r\nadopted sometime in 2008.","keywords":["Floating point arithmetic","standards"],"author":{"@type":"Person","name":"Markstein, Peter","givenName":"Peter","familyName":"Markstein"},"position":20,"pageStart":1,"pageEnd":3,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Markstein, Peter","givenName":"Peter","familyName":"Markstein"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.20","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"},{"@type":"ScholarlyArticle","@id":"#article2020","name":"Towards the Development of an Interval Arithmetic Environment for Validated Computer-Aided Design and Verification of Systems in Control Engineering","abstract":"Modern techniques for the design and analysis of control strategies for nonlinear dynamical systems are often based on the simulation of the open-loop as well as the closed-loop dynamical behavior of suitable mathematical models. In control engineering, continuous-time and discrete-time state-space representations are widely used which are given by sets of ordinary differential equations and difference equations, respectively. In addition to these representations, sets of differential algebraic equations are commonly used. Since we will focus on computational techniques which are applied for the design and mathematical verification of controllers for lumped parameter systems, i.e., systems which do not contain elements with distributed parameters, partial differential equations will not be considered in this talk.\r\n\r\nThe prerequisite for the design and robustness analysis of each control system is the identification of mathematical models which describe the dynamics of the plant to be controlled as well as the available measurement devices with a sufficient accuracy. The model identification task comprises the derivation of physically motivated state equations, their parameterization based on measured data, as well as simplifications to apply specific approaches for controller design. \r\n\r\nIn the design stage, both open-loop and closed-loop control strategies can be considered. Since dynamical system models are subject to uncertain parameters and uncertain initial conditions in most practical applications, detailed mathematical formulations of the desired dynamics of the controlled system are necessary. These specifications involve the definition of robustness with respect to the above-mentioned uncertainties. For linear system representations, robustness is commonly specified in terms of regions in the complex domain containing all admissible poles of the closed-loop transfer functions ($Gamma$-stability) or in terms of specifications of worst-case bounds for the frequency response ($mathcal{B}$-stability) [1]. \r\n\r\nHowever, these specifications do not allow for inclusion of bounds for the state variables which are often available in the time domain if controllers are designed for safety critical applications. Especially for nonlinear dynamical systems, pole assignment based on the linearization of nonlinear mathematical models generally leads to the necessity for the analysis of asymptotic stability of the resulting closed-loop dynamics. \r\n\r\nIn this presentation, we will give an overview of the potential use of validated techniques for the analysis and design of controllers for nonlinear dynamical systems with uncertainties, where the systems under consideration will be subject to constraints for both state and control variables. \r\n\r\nAs an application scenario the design of robust control strategies for a biological wastewater treatment process will be discussed. In the design and the verification process, constraints for both state and control variables which are given by guaranteed interval bounds in the time domain are taken into account. Suitable computational techniques are, for example, based on an extension of the validated initial value problem solver {sc ValEncIA-IVP} [2,6]. For that purpose, differential sensitivities of the trajectories of all state variables with respect to variations of the parameters of the mathematical system model as well as the adaptation of controller parameters are computed. This information can then be used for online identification and adaptation of parameters during the operation of a closed-loop controller as well as in offline design, verification, and optimization. Here, the interval arithmetic routines for sensitivity analysis allow to compute guaranteed differential sensitivity measures for system models with both nominal parameters and interval uncertainties. \r\n\r\nThe presented interval arithmetic techniques are the basis for a general purpose tool for the analysis and the design of robust and optimal control strategies for uncertain dynamical systems. The presentation is concluded with an outlook on the formulation of control problems using sets of differential algebraic equations. Possibilities for the extension of {sc ValEncIA-IVP} to this type of system representation will be summarized. Relations between the presented interval arithmetic approach and methods for stabilizing control of nonlinear dynamical systems which make use of structural system properties such as differential flatness [3] and exact feedback linearization are highlighted [4,5]. In the latter case, input-output linearization as well as (in special cases) input-to-state linearization are of practical importance.\r\n\r\n\r\nReferences:\r\n\r\n[1] J. Ackermann, P. Blue, T. B\"unte, L. G\"uvenc, D. Kaesbauer, M. Kordt, M. Muhler, and D. Odenthal, {it{Robust Control: The Parameter Space Approach}}, Springer--Verlag, London, 2nd edition, 2002.\r\n\r\n[2] E. Auer, A. Rauh, E. P. Hofer, and W. Luther, {it{Validated Modeling of Mechanical Systems with {sc SmartMOBILE}: Improvement of Performance by {sc ValEncIA-IVP}}}, In Proceedings of Dagstuhl Seminar 06021: Reliable Implementation of Real Number Algorithms: Theory and Practice, Lecture Notes in Computer Science, Dagstuhl, Germany, 2006. In print.\r\n\r\n[3] M. Fliess, J. L\u00c3\u0192\u00c2\u00a9vine, P. Martin, and P. Rouchon, {it{Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples}}, International Journal of Control, vol. 61, pp. 1327--1361, 1995.\r\n\r\n[4] H. K. Khalil, {it{Nonlinear Systems}}, Prentice-Hall, Upper Saddle River, New Jersey, 3rd edition, 2002.\r\n\r\n[5] H. J. Marquez, {it{Nonlinear Control Systems}}, John Wiley & Sons, Inc., New Jersey, 2003.\r\n\r\n[6] A. Rauh and E. Auer, {{www.valencia-ivp.com}}.","keywords":["Interval techniques","{sc{ValEncIA-IVP}}","controller design","robustness","validated integration of ODEs","parameter uncertainties","sensitivity analysis"],"author":[{"@type":"Person","name":"Rauh, Andreas","givenName":"Andreas","familyName":"Rauh"},{"@type":"Person","name":"Minisini, Johanna","givenName":"Johanna","familyName":"Minisini"},{"@type":"Person","name":"Hofer, Eberhard P.","givenName":"Eberhard P.","familyName":"Hofer"}],"position":21,"pageStart":1,"pageEnd":10,"dateCreated":"2008-04-22","datePublished":"2008-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Rauh, Andreas","givenName":"Andreas","familyName":"Rauh"},{"@type":"Person","name":"Minisini, Johanna","givenName":"Johanna","familyName":"Minisini"},{"@type":"Person","name":"Hofer, Eberhard P.","givenName":"Eberhard P.","familyName":"Hofer"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08021.21","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume678"}]}