Showing papers by "Zhong-Zhi Bai published in 1998"
TL;DR: The monotone convergence of the parallel matrix multisplitting relaxation method for linear complementarity problems is discussed, and the corresponding comparison theorem about the monotones convergence rate of this method is thoroughly established.
Abstract: The monotone convergence of the parallel matrix multisplitting relaxation method for linear complementarity problems (see Bai, Z. Z. and Evans, D. J. 1997 Int. J. Comput. Math. 63, 309-326) is discussed, and the corresponding comparison theorem about the monotone convergence rate of this method is thoroughly established.
42 citations
TL;DR: In this paper, a class of parallel multisplitting chaotic relaxation methods is established for the large sparse linear complementarity problems, and the global and monotone convergence is proved for the H-matrix and the L -matrix classes, respectively.
27 citations
TL;DR: In this article, the convergence theory of the two-stage iterative method for solving Hermitian positive definite systems of linear equations is studied, and the convergence rate of the splitting matrices and inner iteration number is investigated.
22 citations
TL;DR: Under suitable constraints on the nonlinear multisplitting and the relaxation parameters, the local convergence theory of this class of new methods is established when the Jacobi matrix of the involved nonlinear mapping at the solution point of the non linear complementarity problem is an H-matrix.
12 citations
TL;DR: A class of parallel decomposition-type accelerated over-relaxation methods, including four arbitrary parameters and suitable to the SIMD-systems, is established for solving the large sparse systems of linear equations in this paper, and sufficient conditions ensuring its convergence are deduced when the coefficient matrices of the linear systems of equations are respectively L -matrices, H-matrices and positive definite matrices.
11 citations
TL;DR: This paper presents a class of asynchronous parallel multisplitting two-stage iteration methods for getting their solutions by the high-speed multiprocessor systems, and establishes their local convergence theories.
9 citations
TL;DR: A class of asynchronous parallel nonlinear multisplitting successive overrelaxation (SOR) methods for solving large sparse nonlinear complementarity problems on high-speed MIMD multiprocessor systems is presented.
9 citations
Journal Article•
3 citations
TL;DR: In this paper, the convergence rate of the parallel matrix multisplitting method was investigated for the system of linear equations resulting from the discretization of the one-dimensional Poisson equation.
Abstract: For the system of linear equations resulting from the discretization of the one-dimensional Poisson equation, we investigate the influences of the multiple splittings and the weighting matrices upon the convergence rate of the parallel matrix multisplitting method. The results show that the convergence rate is only dependent on the sizes of the splittings, the degrees of the overlappings, and the distributions of the tasks, but independent of the quantities of the weightings.
1 citations