Solving systems of linear algebraic equations using quasirandom numbers

Abstract

In this paper we analyze a quasi-Monte Carlo method forsolving systems of linear algebraic equations. It is well known that theconvergence of Monte Carlo methods for numerical integration can oftenbe improved by replacing pseudorandom numbers with more uniformlydistributed numbers known as quasirandom numbers. Here the convergenceof a Monte Carlo method for solving systems of linear algebraicequations is studied when quasirandom sequences are used. An errorbound is established and numerical experiments with large sparse matricesare performed using Soboí, Halton and Faure sequences. The resultsindicate that an improvement in both the magnitude of the error andthe convergence rate are achieved.