H-Splittings and Asynchronous Parallel Iterative Methods

Abstract

The paper discusses $H$-splitting and $H$-compatible splitting, furthermore, some properties are given. Asynchronous parallel multisplitting algorithm and its generalization for linear systems $Ax=b$ are established. Convergence of these algorithms is proved under given conditions. The convergent range of relaxation factor $\omega$ is given, numerical example is shown.