Applied Convergence Results of Relaxed Matrix Multisplitting Chaotic Methods for H-Matrices

In this paper, based on the methods presented Song, Yuan [Int. J. Comput. Math., 52 (1994) 195-20, we present relaxed matrix multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze some applied convergence results of methods to be convenient for carrying out numerical experiments.

Relaxed Parallel Modulus-Based Matrix Multisplitting Iterative Methods for Linear Complementarity Problem

In this paper, the authors establish a class of relaxed parallel modulus-based matrix multisplitting iteration methods for large sparse linear complementarity problems, based on the multisplittings of the coefficient matrix. And then, they prove their convergence when the system matrices are H-matrix with positive diagonal elements. These results naturally present convergence conditions for the symmetric positive definite matrices and the M-matrices.

THREE OPTIMIZATION MODELS FOR MULTISPLITTING PRECONDITIONER

In this paper, we use matrix multisplitting with weighting parameters as the preconditioner of A. The optimal weighting parameters are determined by the approaching theory, and the scale of approaching is defined by F-norm, 2-norm, and ∞-norm, respectively. Base on these three minimize models, three algorithms are presented and the convergence theories are established. Finally, numerical examples show that the preconditioner with the optimal weighting parameters, which are obtained from minimize F-norm and 2-norm models, can improve the condition number of A effectively. Besides, general weighting parameters are more effective than non-negative weighting parameters.