Vectorized Monte Carlo solutions of linear equations

Description

Monte Carlo (MC) methods for solving a system of linear equations exhibit high parallelism. The vectorization and incorporation of various sampling methods into the MC methods are investigated to speed up the computations. The weighted sampling method and an alias-like method are found to reduce the order of the time complexity of the MC methods from n[superscript 3], when using the inverse method, to n[superscript 2] for estimating n unknowns. This results into faster solutions with scalar as well as vector processing as demonstrated with computational studies on an IBM 3090-180 computer with a vector facility. The MC methods are shown to be attractive when the number of unknowns is very large and the estimation of only a very small number of unknowns is required.