Parallel Selfverified Method for Solving Linear Systems
Mariana Kolberg, Lucas Baldo, Pedro Isaacsson Velho, Thais Webber, Luiz Gustavo Fernandes, Paulo Fernandes, Dalcídio Moraes Cláudio · 2006
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. 1