38 Search Results for "Luther, Wolfram"

Document
DOI: 10.4230/DagRep.1.9.26
Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)

Authors: Isaac E. Elishakoff, Vladik Kreinovich, Wolfram Luther, and Evgenija D. Popova

Published in: Dagstuhl Reports, Volume 1, Issue 9 (2012)

Abstract
This report documents the program and the results of Dagstuhl Seminar 11371 ``Uncertainty modeling and analysis with intervals -- Foundations, tools, applications'', taking place September 11-16, 2011. The major emphasis of the seminar lies on modeling and analyzing uncertainties and propagating them through application systems by using, for example, interval arithmetic.
Cite as

Isaac E. Elishakoff, Vladik Kreinovich, Wolfram Luther, and Evgenija D. Popova. Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371). In Dagstuhl Reports, Volume 1, Issue 9, pp. 26-57, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@Article{elishakoff_et_al:DagRep.1.9.26,
  author =	{Elishakoff, Isaac E. and Kreinovich, Vladik and Luther, Wolfram and Popova, Evgenija D.},
  title =	{{Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)}},
  pages =	{26--57},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2011},
  volume =	{1},
  number =	{9},
  editor =	{Elishakoff, Isaac E. and Kreinovich, Vladik and Luther, Wolfram and Popova, Evgenija D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.1.9.26},
  URN =		{urn:nbn:de:0030-drops-33181},
  doi =		{10.4230/DagRep.1.9.26},
  annote =	{Keywords: Uncertainty modeling, Interval arithmetic, Imprecise probabilities, Sensitivity analysis, mechatronics, bioinformatics and finance}
}
Document
DOI: 10.4230/DagSemProc.09471.3
Interval Approaches to Reliable Control of Dynamical Systems

Authors: Andreas Rauh and Ekaterina Auer

Published in: Dagstuhl Seminar Proceedings, Volume 9471, Computer-assisted proofs - tools, methods and applications (2010)

Abstract
Recently, we presented an implementation of interval-based algorithms which can be applied in real-time to control dynamical processes and to estimate internal states and disturbances. The approach is based on verified methods for sets of algebraic equations, ordinary differential equations as well as differential-algebraic equations. Due to this fact, the same program code can be used for two different tasks. On the one hand, we can use it online to estimate non-measurable internal system states which are necessary for nonlinear model-based control strategies. On the other hand, we can verify the admissibility and feasibility of these control strategies offline. Although we use the same code for the online and offline tasks, there is an important difference between them. While the computing time is of minor importance in offline applications, we have to guarantee that the necessary online computations are completed successfully in a predefined time interval. For that reason, the role of verification is slightly different depending on the task. In offline applications, our goal is to compute tightest possible bounds for the sets of all solutions to the control problem under consideration. In contrast to that, we restrict the online mode to a search for a single solution that matches all demands on feasibility of control inputs and admissibility of the trajectories of the state variables in a reliable way. To highlight the practical applicability of the underlying computational routines, we present the following cases for the use of verified solvers in real-time [1-3]. Case 1: Direct computation of feedforward control strategies with the help of differential-algebraic equation solvers. In this application, both verified and non-verified solvers can be used to determine open-loop control strategies for a dynamical system such that its output coincides with a predefined time response within given tolerances. This procedure corresponds to a numerical inversion of the dynamics of the system to be controlled. In this case, verified solvers are used to prove the existence of a control law within given physical bounds for the admissible range of the system inputs. Case 2: If measured data and their time derivatives are available, the same procedures as in case 1 can be used to estimate non-measured state variables as well as non-measurable disturbances. Since the verified algorithms used in this context are capable of propagating bounded measurement uncertainties, the quality of the state and disturbance estimates can be expressed in terms of the resulting interval widths. Moreover, assumptions about the parameters and the structure of the underlying model can be verified. Case 3: Routines for verified sensitivity analysis provide further information on the influence of variations of control inputs on the trajectories of the state variables. We present novel procedures implementing a sensitivity-based framework for model-predictive control. These procedures can be integrated directly in a feedback control structure. Sometimes it is necessary to combine verified and non-verified algorithms to solve a given control problem. In this case, it is important to certify the results of the algorithm appropriately. Based on the four-tier hierarchy presented in earlier works [4], we develop a measure for characterizing such mixed approaches. The presentation is concluded with simulation and experimental results for the example of temperature control of a distributed heating system. [1] Rauh, Andreas; Auer, Ekaterina: Applications of Verified DAE Solvers in Engineering, Intl. Workshop on Verified Computations and Related Topics, COE Lecture Note Vol. 15: Kyushu University, pp. 88-96, Karlsruhe, Germany, 2009. [2] Rauh, Andreas; Menn, Ingolf; Aschemann, Harald: Robust Control with State and Disturbance Estimation for Distributed Parameter Systems, Proc. of 15th Intl. Workshop on Dynamics and Control 2009, pp. 135-142, Tossa de Mar, Spain, 2009. [3] Rauh, Andreas; Auer, Ekaterina; Aschemann, Harald: Real-Time Application of Interval Methods for Robust Control of Dynamical Systems, CD-Proc. of IEEE Intl. Conference on Methods and Models in Automation and Robotics MMAR 2009, Miedzyzdroje, Poland, 2009. [4] Auer, Ekaterina; Luther, Wolfram: Numerical Verification Assessment in Computational Biomechanics, in A. Cuyt, W. Krämer, W. Luther, P. Markstein: Numerical Validation in Current Hardware Architectures, LNCS 5492, pp. 145-160, Springer-Verlag, Berlin, Heidelberg, 2009.
Cite as

Andreas Rauh and Ekaterina Auer. Interval Approaches to Reliable Control of Dynamical Systems. In Computer-assisted proofs - tools, methods and applications. Dagstuhl Seminar Proceedings, Volume 9471, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{rauh_et_al:DagSemProc.09471.3,
  author =	{Rauh, Andreas and Auer, Ekaterina},
  title =	{{Interval Approaches to Reliable Control of Dynamical Systems}},
  booktitle =	{Computer-assisted proofs - tools, methods and applications},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9471},
  editor =	{B. Malcolm Brown and Erich Kaltofen and Shin'ichi Oishi and Siegfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09471.3},
  URN =		{urn:nbn:de:0030-drops-25120},
  doi =		{10.4230/DagSemProc.09471.3},
  annote =	{Keywords: Robust control, Ordinary differential equations, Differential-algebraic equations}
}
Document
DOI: 10.4230/DagSemProc.09471.4
Verification and Validation for Femur Prosthesis Surgery

Authors: Ekaterina Auer, Roger Cuypers, Eva Dyllong, Stefan Kiel, and Wolfram Luther

Published in: Dagstuhl Seminar Proceedings, Volume 9471, Computer-assisted proofs - tools, methods and applications (2010)

Abstract
In this paper, we describe how verified methods we are developing in the course of the project TellHim&S (Interval Based Methods For Adaptive Hierarchical Models In Modeling And Simulation Systems) can be applied in the context of the biomechanical project PROREOP (Development of a new prognosis system to optimize patient-specific pre- operative surgical planning for the human skeletal system). On the one hand, it includes the use of verified hierarchical structures for reliable geometric modeling, object decomposition, distance computation and path planning. On the other hand, we cover such tasks as verification and validation assessment and propagation of differently described uncertainties through system models in engineering or mechanics.
Cite as

Ekaterina Auer, Roger Cuypers, Eva Dyllong, Stefan Kiel, and Wolfram Luther. Verification and Validation for Femur Prosthesis Surgery. In Computer-assisted proofs - tools, methods and applications. Dagstuhl Seminar Proceedings, Volume 9471, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{auer_et_al:DagSemProc.09471.4,
  author =	{Auer, Ekaterina and Cuypers, Roger and Dyllong, Eva and Kiel, Stefan and Luther, Wolfram},
  title =	{{Verification and Validation for Femur Prosthesis Surgery}},
  booktitle =	{Computer-assisted proofs - tools, methods and applications},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9471},
  editor =	{B. Malcolm Brown and Erich Kaltofen and Shin'ichi Oishi and Siegfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09471.4},
  URN =		{urn:nbn:de:0030-drops-25133},
  doi =		{10.4230/DagSemProc.09471.4},
  annote =	{Keywords: Graphical interface construction, superquadrics, 3D modeling, biomedical engineering}
}
Document
DOI: 10.4230/DagSemProc.08021.1
08021 Abstracts Collection – Numerical Validation in Current Hardware Architectures

Authors: Wolfram Luther, Annie Cuyt, Walter Krämer, and Peter Markstein

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

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. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Wolfram Luther, Annie Cuyt, Walter Krämer, and Peter Markstein. 08021 Abstracts Collection – Numerical Validation in Current Hardware Architectures. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{luther_et_al:DagSemProc.08021.1,
  author =	{Luther, Wolfram and Cuyt, Annie and Kr\"{a}mer, Walter and Markstein, Peter},
  title =	{{08021 Abstracts Collection – Numerical Validation in Current Hardware Architectures}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--31},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.1},
  URN =		{urn:nbn:de:0030-drops-14785},
  doi =		{10.4230/DagSemProc.08021.1},
  annote =	{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}
}
Document
DOI: 10.4230/DagSemProc.08021.2
08021 Summary – Numerical Validation in Current Hardware Architectures

Authors: Annie Cuyt, Walter Krämer, Wolfram Luther, and Peter Markstein

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
Numerical validation in current hardware architectures - From embedded system to high-end computational grids Topics List of participants Schedule List of talks
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Annie Cuyt, Walter Krämer, Wolfram Luther, and Peter Markstein. 08021 Summary – Numerical Validation in Current Hardware Architectures. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{cuyt_et_al:DagSemProc.08021.2,
  author =	{Cuyt, Annie and Kr\"{a}mer, Walter and Luther, Wolfram and Markstein, Peter},
  title =	{{08021 Summary – Numerical Validation in Current Hardware Architectures}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.2},
  URN =		{urn:nbn:de:0030-drops-14334},
  doi =		{10.4230/DagSemProc.08021.2},
  annote =	{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}
}
Document
DOI: 10.4230/DagSemProc.08021.3
A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range

Authors: Frithjof Blomquist, Werner Hofschuster, and Walter Krämer

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double format) and fast floating point operations as well as exact dot product computations. Due to floating point limitations it is not an arbitrary precision arithmetic. However, it typically allows computations using several hundred mantissa digits. A set of new modified staggered arithmetics for real and complex data as well as for real interval and complex interval data with very wide exponent range is presented. Some applications show the increased accuracy of computed results compared to ordinary staggered interval computations. The very wide exponent range of the new arithmetic operations allows computations far beyond the IEEE data formats. The new arithmetics would be extremly fast, if an exact dot product was available in hardware (the fused accumulate and add instruction is only one step in this direction).
Cite as

Frithjof Blomquist, Werner Hofschuster, and Walter Krämer. A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{blomquist_et_al:DagSemProc.08021.3,
  author =	{Blomquist, Frithjof and Hofschuster, Werner and Kr\"{a}mer, Walter},
  title =	{{A Modified Staggered Correction Arithmetic  with Enhanced Accuracy and Very Wide Exponent Range}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--23},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.3},
  URN =		{urn:nbn:de:0030-drops-14454},
  doi =		{10.4230/DagSemProc.08021.3},
  annote =	{Keywords: Staggered correction, multiple precision, C-XSC, interval computation, wide exponent range, reliable numerical computations, complex interval funct}
}
Document
DOI: 10.4230/DagSemProc.08021.4
A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC

Authors: Mariana Kolberg, Walter Krämer, and Michael Zimmer

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
C-XSC is a powerful C++ class library which simplifies the development of 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. In 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 × 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. The 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 environments. 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.
Cite as

Mariana Kolberg, Walter Krämer, and Michael Zimmer. A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kolberg_et_al:DagSemProc.08021.4,
  author =	{Kolberg, Mariana and Kr\"{a}mer, Walter and Zimmer, Michael},
  title =	{{A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.4},
  URN =		{urn:nbn:de:0030-drops-14479},
  doi =		{10.4230/DagSemProc.08021.4},
  annote =	{Keywords: C-XSC, reliable computing, 100-digit challenge, reliable linear system solver, high performance computing, large dense linear systems}
}
Document
DOI: 10.4230/DagSemProc.08021.5
A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling

Authors: Eva Dyllong

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
Techniques of reliable computing like interval arithmetic can be used to guarantee a reliable solution even in the presence of numerical round-off errors. The need to trace bounds for the error function separately can be eliminated using these techniques. In this talk, we focus on some demonstrations how the techniques and algorithms of reliable computing can be applied to the construction and further processing of hierarchical solid representations using the octree model as an example. An octree is a common hierarchical data structure to represent 3D geometrical objects in solid modeling systems or to reconstruct a real scene. The solid representation is based on recursive cell decompositions of the space. Unfortunately, the data structure may require a large amount of memory when it uses a set of very small cubic nodes to approximate a solid. In this talk, we present a novel generalization of the octree model created from a CSG object that uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on the boundary or outside the object to handle whole sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. Furthermore, this talk is concerned with interval-based algorithms for reliable proximity queries between the extended octrees and with further processing of the structure. We conclude the talk with some examples of implementations.
Cite as

Eva Dyllong. A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{dyllong:DagSemProc.08021.5,
  author =	{Dyllong, Eva},
  title =	{{A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.5},
  URN =		{urn:nbn:de:0030-drops-14408},
  doi =		{10.4230/DagSemProc.08021.5},
  annote =	{Keywords: Reliable solid modeling, hierarchical data structure}
}
Document
DOI: 10.4230/DagSemProc.08021.6
A Software Library for Reliable Online-Arithmetic with Rational Numbers

Authors: Gregorio de Miguel Casado and Juan Manuel García Chamizo

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
An overview of a novel calculation framework for scientific computing in integrable spaces is introduced. This paper discusses some implementation issues adopted for a software library devoted to exact rational online-arithmetic operators for periodic rational operands codified in fractional positional notation.
Cite as

Gregorio de Miguel Casado and Juan Manuel García Chamizo. A Software Library for Reliable Online-Arithmetic with Rational Numbers. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{demiguelcasado_et_al:DagSemProc.08021.6,
  author =	{de Miguel Casado, Gregorio and Garc{\'\i}a Chamizo, Juan Manuel},
  title =	{{A Software Library for Reliable Online-Arithmetic with Rational Numbers}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.6},
  URN =		{urn:nbn:de:0030-drops-14392},
  doi =		{10.4230/DagSemProc.08021.6},
  annote =	{Keywords: Computable analysis, online-arithmetic, rational numbers}
}
Document
DOI: 10.4230/DagSemProc.08021.7
C-XSC and Closely Related Software Packages

Authors: Werner Hofschuster, Walter Krämer, and Markus Neher

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
C-XSC and Closely Related Software Packages
Cite as

Werner Hofschuster, Walter Krämer, and Markus Neher. C-XSC and Closely Related Software Packages. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{hofschuster_et_al:DagSemProc.08021.7,
  author =	{Hofschuster, Werner and Kr\"{a}mer, Walter and Neher, Markus},
  title =	{{C-XSC and Closely Related Software Packages}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.7},
  URN =		{urn:nbn:de:0030-drops-14425},
  doi =		{10.4230/DagSemProc.08021.7},
  annote =	{Keywords: Mathematical software, reliable computing, C-XSC, CoStLy, ACETAF}
}
Document
DOI: 10.4230/DagSemProc.08021.8
Complete Interval Arithmetic and its Implementation

Authors: Ulrich Kulisch

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
A Complete Interval Arithmetic and its Implementation is discussed.
Cite as

Ulrich Kulisch. Complete Interval Arithmetic and its Implementation. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kulisch:DagSemProc.08021.8,
  author =	{Kulisch, Ulrich},
  title =	{{Complete Interval Arithmetic and its Implementation}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.8},
  URN =		{urn:nbn:de:0030-drops-14461},
  doi =		{10.4230/DagSemProc.08021.8},
  annote =	{Keywords: Interval Arithmetic, implementation}
}
Document
DOI: 10.4230/DagSemProc.08021.9
Distributed parameter and state estimation in a network of sensors

Authors: Michel Kieffer

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

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.
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Michel Kieffer. Distributed parameter and state estimation in a network of sensors. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kieffer:DagSemProc.08021.9,
  author =	{Kieffer, Michel},
  title =	{{Distributed parameter and state estimation in a network of sensors}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.9},
  URN =		{urn:nbn:de:0030-drops-14440},
  doi =		{10.4230/DagSemProc.08021.9},
  annote =	{Keywords: Parameter estimation, state estimation, bounded errors, nonlinear estimation}
}
Document
DOI: 10.4230/DagSemProc.08021.10
Extending the Range of C-XSC: Some Tools and Applications for the use in Parallel and other Environments

Authors: Markus Grimmer

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
There is a broad range of packages and libraries for verified numerical computation. C-XSC is a library combining one of the most extensive sets of functions and operations on the one hand with a wide range of applications and special features on the other hand. As such it is an important task both to make use of its existing capabilities in applications and to develop further extensions giving access to additional areas and environments. In this talk, we present some examples of extensions for C-XSC that have been developed lately. Among these are extensions that give access to further hardware and software environments as well as applications making use of these possibilities. Software libraries for interval computation always imply great computation effort: One way to reduce computation times is the development of parallel methods to make use of parallel hardware. For this, it is important that the features and data types of the used library can be easily used in parallel programs. An MPI package for C-XSC data types allows to easily use C-XSC in parallel programs without bothering about the internal structure of data types. Another extension of C-XSC, the C-XSC Taylor arithmetic, is also covered by the MPI package. Parallel verified linear system solvers based on the package are available as well, and further development has been and is being done to integrate more efficient methods for interval linear system solution. One application making use of the mentioned extensions is a parallel verified Fredholm integral equation solver. Some results are given to demonstrate the reduction of computation time and, at the same time, the accuracy gain that can be obtained using the increased computation power. Naturally, hardware interval support would offer still more possibilities towards optimal performance of verified numerical software. Another possibility to extend the range of C-XSC is to make results available for further computations in other software environments as, for example, computer algebra packages. An example of this is presented for the Maple interval package intpakX. This kind of interfaces also allows the user to get access to further platforms like operating systems, compilers or even hardware. References: [1] ALiCEnext: http://www.alicenext.uni-wuppertal.de. [2] Blomquist, F.; Hofschuster, W.; Kraemer, W.: Real and Complex Taylor Arithmetic in C-XSC. Preprint BUW-WRSWT 2005/4, University of Wuppertal, 2005. [3] Grimmer, M.; Kraemer, W.: An MPI Extension for Verified Numerical Computations in Parallel Environments. In: Int. Conf. on Scientific Computing (CSC’07, Worldcomp’07) Las Vegas, June 25-28, 2007, Proceedings pp. 111-117, Arabnia et al. (eds.), 2007. [4] Grimmer, M.: An MPI Extension for the Use of C-XSC in Parallel Environments. Preprint BUW-WRSWT 2005/3, University of Wuppertal, 2005. [5] Grimmer, M.: Selbstverifizierende mathematische Softwarewerkzeuge im High Performance Computing. Dissertation, Logos Verlag, Berlin, 2007. [6] Grimmer, M.: Interval Arithmetic in Maple with intpakX. In: PAMM - Proceedings in Applied Mathematics and Mechanics, Vol. 2, Nr. 1, p. 442-443, Wiley-InterScience, 2003. [7] Hofschuster, W.; Kraemer, W.: C-XSC 2.0: A C++ Library for Extended Scientific Computing. Numerical Software with Result Verification, Lecture Notes in Computer Science, Volume 2991/2004, Springer-Verlag, Heidelberg, pp. 15 - 35, 2004. [8] Klein, W.: Enclosure Methods for Linear and Nonlinear Systems of Fredholm Integral Equations of the Second Kind. In: Adams, Kulisch: Scientific Computing with Result Verification, Academic Press, 1993.
Cite as

Markus Grimmer. Extending the Range of C-XSC: Some Tools and Applications for the use in Parallel and other Environments. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{grimmer:DagSemProc.08021.10,
  author =	{Grimmer, Markus},
  title =	{{Extending the Range of C-XSC: Some Tools and Applications for the use in Parallel and other Environments}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.10},
  URN =		{urn:nbn:de:0030-drops-14416},
  doi =		{10.4230/DagSemProc.08021.10},
  annote =	{Keywords: C-XSC, Integral Equations, Interval Arithmetic, Maple, MPI, Parallel Environment, Taylor Arithmetic, Verified Linear System Solver.}
}
Document
DOI: 10.4230/DagSemProc.08021.11
Fast (Parallel) Dense Linear Interval Systems Solvers in C-XSC Using Error Free Transformations and BLAS

Authors: Michael Zimmer and Walter Krämer

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
The traditional solver for linear interval systems available in C-XSC [6,1] is mathematically based on the Krawczyk[12] operator and modifications introduced by Rump[17]. The Krawczyk operator is composed of matrix/vector operations. These operations are realized in C-XSC with higest accuracy (only one final rounding) using a so called long accumulator (dotprecision variable). C-XSC dotprecision variables allow the error free computation of sums of floating point numbers as well as the error free computation of scalar products of floating point vectors. Thus, from a mathematical point of view these operations are perfect. Because actual hardware does not support these perfect scalar products all operations have to be realized by software. This fact leads to a tremendous time penalty (note: it has been shown that with modest additional hardware costs perfect scalar products can be made as fast as simple floating-point loops). To speed up the C-XSC scalar product software-operations we adapt the so called DotK algorithm as published in [14]. Error free transformations[14,3,4,10] are used as basic building blocks to develop summation and scalar product algorithms simulating a K-fold precision. Compared to the perfect C-XSC operations these operations are fast. They are more accurate than simple floating-point loops (but of course no longer perfect in the mathematical sense). The fast operations are available in C-XSC via the new data types DotK, IDotK, CDotk and CIDotK. These new data types are composed in such a way that traditional C-XSC code using dotprecision variables can be adapted with minimal effort. It is possible to switch (at runtime!) from perfect computations to fast operations using K-fold precision (K equal 0 means traditional dotprecision computations) and it is possible to hold intermediate results with corresponding error bounds for further summations or scalar product updates. The details are described in [19]. Additionaly, based on similar algorithms used in Intlab[16], BLAS and LAPACK libraries [2] are used in the O(n³) parts of the linear system solver. For matrix-matrix products, manipulation of the rounding mode of the processor is used to compute enclosures of the correct result. Comparing the traditional solver with the new version shows that the class of problems which are solvable with the new version is smaller than the class of problems which can be solved using the solver based on perfect operations. But it seems that for real world problems also the new solver is appropriate. Using the new solver based on BLAS and simulating a quadrupel precision (i.e. k==2) the speedup comes close to 200(!). The new solver is nearly as fast as the corresponding IntLab[16] solver verifylss. Solving a real linaer system of dimension 1000 on a Pentium 4 with 3.2GHz takes about 2.8 seconds. In all cases tested the accuracy of our new solver was better and in some cases significantly better than the accuracy of the corresponding IntLab results. The new solver also allows solving larger (dense) problems than its IntLab counterpart. We also show some examples where IntLab falls down whereas our new solver still works. A parallel version of this solver, based on ScaLAPACK, is also available. Unlike the previous parallel solver in C-XSC[5], this new solver does not depend on a root-node, which makes it possible to compute a verified solution even of very large linear systems. In the talk we will discuss the new data types in more detail, we will emphasize our modifications to the DotK algorithm taken from the literature [14,15], we will show time measurements and we will present results concerning the accuracy of the computed enclosures. Our results will also be compared to corresponding results computed with the IntLab package. We also will comment on hardware features and compiler options which can/should be used to get reliable results on different platforms efficiently. References: [1] Downloads: C-XSC library: http://www.math.uni-wuppertal.de/~xsc/xsc/cxsc.html Solvers: http://www.math.uni-wuppertal.de/~xsc/xsc/cxsc_software.html [2] L.S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, R. C. Whaley, An Updated Set of Basic Linear Algebra Subprograms (BLAS), ACM Trans. Math. Soft., 28-2 (2002), pp. 135--151. [3] Bohlender, G.; Walter, W.; Kornerup, P.; Matula, D.W.; Kornerup, P.; Matula, D.W.: Semantics for Exact Floating Point Operations. Proceedings, 10th IEEE Symposium on Computer Arithmetic, 26-28 June 1991, IEEE, 1991. [4] Dekker, T.J.: A floating-point technique for extending the available precision. Numer. Math., 18:224, 1971. [5] Grimmer, M.: Selbstverifizierende Mathematische Softwarewerkzeuge im High-Performance Computing. Konzeption, Entwicklung und Analyse am Beispiel der parallelen verifizierten Loesung linearer Fredholmscher Integralgleichungen zweiter Art. Logos Verlag, 2007. [6] Hofschuster, W.; Kraemer, W.: C-XSC 2.0: A C++ Library for Extended Scientific Computing. Numerical Software with Result Verification, Lecture Notes in Computer Science, Volume 2991/2004, Springer-Verlag, Heidelberg, pp. 15 - 35, 2004. [7] Kersten, Tim: Verifizierende rechnerinvariante Numerikmodule, Dissertation, University of Karlsruhe, 1998 [8] Klatte, Kulisch, Wiethoff, Lawo, Rauch: "C-XSC - A C++ Class Library for Extended Scientific Computing", Springer-Verlag, Heidelberg, 1993. Due to the C++ standardization (1998) and dramatic changes in C++ compilers over the last years this documentation describes no longer the actual C-XSC environment. Please refer to more accurate documentation (e.g.[1]) available from the web site of our research group: http... [9] Kirchner, R., Kulisch, U.: Hardware Support for Interval Arithmetic. Reliable Computing, Volume 12, Number 3, June 2006 , pp. 225-237(13). [10] Knuth, D.E.: The Art of Computer Programming: Seminumerical Algorithms. Addison Wesley, 1969, vol. 2. [11] Kulisch, U.: Computer Arithmetic and Validity - Theory, Implementation. To appear. [12] Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing, 4:187-201, 1969. [13] Lerch, M.; Tischler, G.; Wolff von Gudenberg, J.; Hofschuster, W; Kraemer, W.: filib++, a Fast Interval Library Supporting Containment Computations. ACM TOMS, volume 32, number 2, pp. 299-324, 2006. [14] Ogita, T., Rump, S.M., Oishi, S.: Accurate sum and dot product. SIAM Journal on Scientific Computing, 26:6, 2005. [15] Oishi, S., Tanabe, K., Ogita, T., Rump, S.M., Yamanaka, N.: A Parallel Algorithm of Accurate Dot Product. Submitted for publication, 2007. [16] Rump, S.M.: Intlab - Interval Laboratory. Developments in Reliable Computing, pp. 77-104, 1999. [17] Rump, S.M.: Kleine Fehlerschranken bei Matrixproblemen, Dissertation, University of Karlsruhe, 1980 [18] Stroustrup, Bjarne: The C++-Programming Language, 3rd Edition, Addison-Wesley, 2000. [19] Zimmer, Michael: Laufzeiteffiziente, parallele Loeser fuer lineare Intervallgleichungssysteme in C-XSC, Master thesis, University of Wuppertal, 2007. AMS subject classification: 65H10, 15-04, 65G99, 65G10, 65-04
Cite as

Michael Zimmer and Walter Krämer. Fast (Parallel) Dense Linear Interval Systems Solvers in C-XSC Using Error Free Transformations and BLAS. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{zimmer_et_al:DagSemProc.08021.11,
  author =	{Zimmer, Michael and Kr\"{a}mer, Walter},
  title =	{{Fast (Parallel) Dense Linear Interval Systems Solvers in C-XSC Using Error Free Transformations and BLAS}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.11},
  URN =		{urn:nbn:de:0030-drops-14365},
  doi =		{10.4230/DagSemProc.08021.11},
  annote =	{Keywords: Error-free transformations, K-fold accuracy, accurate dot product, C-XSC, high accuracy, dense linear systems, verified computation.}
}
Document
DOI: 10.4230/DagSemProc.08021.12
Implementation of the reciprocal square root in MPFR

Authors: Paul Zimmermann

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract
We describe the implementation of the reciprocal square root --- also called inverse square root --- as a native function in the MPFR library. The difficulty is to implement Newton's iteration for the reciprocal square root on top's of GNU MP's extsc{mpn} layer, while guaranteeing a rigorous $1/2$ ulp bound on the roundoff error.
Cite as

Paul Zimmermann. Implementation of the reciprocal square root in MPFR. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{zimmermann:DagSemProc.08021.12,
  author =	{Zimmermann, Paul},
  title =	{{Implementation of the reciprocal square root in MPFR}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.12},
  URN =		{urn:nbn:de:0030-drops-14357},
  doi =		{10.4230/DagSemProc.08021.12},
  annote =	{Keywords: Multiple precision, floating-point, inverse square root, correct rounding, MPFR library}
}
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