Parallel Selfverified Method for Solving Linear Systems
Mariana Kolberg (PUCRS - PPGCC)Lucas Baldo (PUCRS - PPGCC)
Pedro Velho (PUCRS - PPGCC)
Thais Webber (PUCRS - PPGCC)
Paulo Fernandes (PUCRS - PPGCC)
Dalcidio Claudio (PUCRS - PPGCC)
Abstract:
This paper presents the parallelization of a self-verified method for solving dense linear equations. Verified
computing provides an interval result that surely contains the correct result. The advent of parallel computing and its
impact in the overall performance of various algorithms on numerical analysis have been increasing in the last decade.
Two main points of this method, which demand a higher computational cost, were carried out: the backward/forward
substitution of a LU-decomposed matrix A and an iterative refinement step. Our main contribution is to point out the
advantages an drawbacks of our approach, in order to popularize the use of self-verified computation.
Keywords:
Cluster and Grid Computing, Numerical Methods (Linear algebra), Parallel and Distributed Computing
