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Documents authored by Kolberg, Mariana

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.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.08021.13
Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation

Authors: Mariana Kolberg, Gerd Bohlender, and Dalcidio Claudio

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

Abstract
A parallel version of the self-verified method for solving linear systems was presented on PARA and VECPAR conferences in 2006. In this research we propose improvements aiming at a better performance. The idea is to implement an algorithm that uses technologies as MPI communication primitives associated to libraries as LAPACK, BLAS and C-XSC, aiming to provide both self-verification and speed-up at the same time. The algorithms should find an enclosure even for very ill-conditioned problems. In this scenario, a parallel version of a self-verified solver for dense linear systems appears to be essential in order to solve bigger problems. Moreover, the major goal of this research is to provide a free, fast, reliable and accurate solver for dense linear systems.
Cite as

Mariana Kolberg, Gerd Bohlender, and Dalcidio Claudio. Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kolberg_et_al:DagSemProc.08021.13,
  author =	{Kolberg, Mariana and Bohlender, Gerd and Claudio, Dalcidio},
  title =	{{Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--5},
  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.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.13},
  URN =		{urn:nbn:de:0030-drops-14386},
  doi =		{10.4230/DagSemProc.08021.13},
  annote =	{Keywords: Linear systems, result verification, parallel computing}
}
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