Kolberg, Mariana ;
Krämer, Walter ;
Zimmer, Michael
A Note on Solving Problem 7 of the SIAM 100Digit Challenge Using CXSC
Abstract
CXSC is a powerful C++ class library which simplifies the development
of selfverifying numerical software. But CXSC 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 100digit challenge. To get the result we have to solve a 20 000 Ãƒâ€” 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 CXSC 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.
BibTeX  Entry
@InProceedings{kolberg_et_al:DSP:2008:1447,
author = {Mariana Kolberg and Walter Kr{\"a}mer and Michael Zimmer},
title = {A Note on Solving Problem 7 of the SIAM 100Digit Challenge Using CXSC},
booktitle = {Numerical Validation in Current Hardware Architectures},
year = {2008},
editor = {Annie Cuyt and Walter Kr{\"a}mer and Wolfram Luther and Peter Markstein},
number = {08021},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1447},
annote = {Keywords: CXSC, reliable computing, 100digit challenge, reliable linear system solver, high performance computing, large dense linear systems}
}
2008
Keywords: 

CXSC, reliable computing, 100digit challenge, reliable linear system solver, high performance computing, large dense linear systems 
Seminar: 

08021  Numerical Validation in Current Hardware Architectures

Related Scholarly Article: 


Issue date: 

2008 
Date of publication: 

2008 