Premium
An efficient approach to solve very large dense linear systems with verified computing on clusters
Author(s) -
Kolberg Mariana,
Bohlender Gerd,
Fernandes Luiz Gustavo
Publication year - 2015
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1950
Subject(s) - solver , computer science , computation , linear system , enclosure , context (archaeology) , interval (graph theory) , interval arithmetic , algorithm , parallel computing , computational science , mathematics , mathematical analysis , telecommunications , paleontology , combinatorics , bounded function , biology , programming language
Summary Automatic result verification is an important tool to guarantee that completely inaccurate results cannot be used for decisions without getting remarked during a numerical computation. Mathematical rigor provided by verified computing allows the computation of an enclosure containing the exact solution of a given problem. Particularly, the computation of linear systems can strongly benefit from this technique in terms of reliability of results. However, in order to compute an enclosure of the exact result of a linear system, more floating‐point operations are necessary, consequently increasing the execution time. In this context, parallelism appears as a good alternative to improve the solver performance. In this paper, we present an approach to solve very large dense linear systems with verified computing on clusters. This approach enabled our parallel solver to compute huge linear systems with point or interval input matrices with dimensions up to 100,000. Numerical experiments show that the new version of our parallel solver introduced in this paper provides good relative speedups and delivers a reliable enclosure of the exact results. Copyright © 2014 John Wiley & Sons, Ltd.