Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation
Mariana Kolberg (PPGCC- Pontificia Universidade Católica do Rio Grande do Sul)Gerd Bohlender (Institut für Angewandte und Numerische Mathematik, Universität Karlsruhe)
Dalcidio Claudio (PPGCC- Pontificia Universidade Católica do Rio Grande do Sul)
Abstract:
A parallel version of the self-verified method for solving linear
systems was presented in previous publications. 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.
Keywords:
Parallel and Distributed Computing, Cluster Computing, Numerical Algorithms for CS&E
