Convergence of the matrix multi-splitting multi-parameter relaxation methods

Abstract

D. J. Evans, Wang Deren and Bai Zhongzhi [1] have recently proposed a class of matrix multi-splitting multi-parameter relaxation methods to solve a large linear system Ax = b. In this paper, using our results on the norm of the diagonally similar matrix together with the result on the upper bound of the norm ∥M ⁻¹ N ∥∞ of the matrix M ⁻¹ N given by Hu Jia-gan, we obtain further results on the sufficient condition of the above-mentioned matrix multi-splitting multi-parameter relaxation method to converge, thus greatly developing the convergence theory previously established in [1].

Keywords:

• Multi-splitting
• parallel computation
• relaxation method
• convergence