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

• Published in: High Performance Computing for Computational Science - VECPAR 2008 pp. 13 - 26
• Main Authors: Kolberg, Mariana, Bohlender, Gerd, Claudio, Dalcidio
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2008
• Series: Lecture Notes in Computer Science
• Subjects: Numerical algorithms for CS&E; Parallel or Distributed Computation and Cluster Computation
• ISBN: 3540928588; 9783540928584
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-92859-1_3

A parallel version of the self-verified method for solving linear systems was presented in [20, 21]. 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 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.