Solving dense interval linear systems with verified computing on multicore architectures

Abstract

Automatic result verification is an important tool to reduce the impact of floating-point errors in numerical computation and to guarantee the mathematical rigor of results. One fundamental problem in Verified Computing is to find an enclosure that surely contains the exact result of a linear system. Many works have been developed to optimize Verified Computing algorithms using parallel programming techniques and message passing paradigm on clusters of computers. However, the High Performance Computing scenario changed considerably with the emergence of multicore architectures in the past few years. This paper presents an ongoing research project which has the purpose of developing a self-verified solver for dense interval linear systems optimized for parallel execution on these new architectures. The current version has obtained up to 85% of reduction at execution time and a speedup of 6.70 when solving a 15,000 × 15,000 interval linear system on an eight core computer. © 2011 Springer-Verlag Berlin Heidelberg.