Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization

Abstract

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an $H$-matrix or a symmetric positive definite matrix. First, $m$ parallel iterations are implemented in $m$ different processors. Second, based on $l_1$-norm or $l_2$-norm, the $m$ optimization models are parallelly treated in $m$ different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numerical examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.