Convergence of relaxed parallel multisplitting methods with different weighting schemes1

摘要

Multisplitting methods are parallel methods for the solution of a linear system Ax=b. It has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation and some different weighting other than the traditional postweighting are used. In this paper, by using a result on extrapolation method (cf. Lemma 6 below) and the comparison theorem of Elsner (L. Elsner Numer. Math. 56 (1989) 283–289) we study the convergence of two different variants of relaxed multisplitting methods with different weighting schemes. The results obtained considerably improve and generalize the previous ones. Moreover, some comparison theorems are also presented when A is a monotone matrix or an M-matrix.