Zhong-Zhi Bai

TL;DR: In this article, a banded M-splitting iteration method is proposed to compute approximate solutions for the corresponding discrete linear systems resulting from certain finite difference schemes at every temporal level and demonstrate its asymptotic convergence without imposing any extra condition.

TL;DR: In this paper, both local and global convergence properties of the multisplitting two-stage iterative method (Numer. 15 (1997) 347) are further studied in depth when A∈ R n×n is symmetric positive definite and its multiple splittings are symmetric P-regular.

TL;DR: The convergence properties of a variant of the parallel chaotic multisplitting iteration method for solving large sparse systems of linear equations are discussed, and the monotone convergence theory and themonotone comparison theorem about this method are established.

TL;DR: An exact closed-form formula is conducted for the mean-squared residual of the iterate generated by the randomized Gauss-Seidel method, and an upper bound for the convergence rate of the randomizedGauss- Seidel method is estimated.

TL;DR: Both theoretical analysis and numerical experiments show that the preconditioned Krylov subspace iteration methods can exhibit optimal convergence property in the sense that their convergence rates are independent of both discretization stepsizes and problem parameters, and their computational workloads are linearly proportional with the number of discrete unknowns.