Non-stationary Parallel Multisplitting Two-Stage Iterative Methods with Self-AdaptiveWeighting Schemes

Abstract

In this paper, we study the non-stationary parallel multisplitting two-stage iterative methods with selfadaptive weighting matrices for solving a linear system whose coefficient matrix is symmetric positive definite. Two choices of Self-adaptive weighting matrices are given, especially, the nonnegativity is eliminated. Moreover, we prove the convergence of the non-stationary parallel multisplitting two-stage iterative methods with self-adaptive weighting matrices. Finally, the numerical comparisons of several self-adaptive nonstationary parallel multisplitting two-stage iterative methods are shown.