Zhong-Zhi Bai

TL;DR: A two-step preconditioning strategy based on the banded matrix approximation (BMA) and the alternating direction implicit (ADI) iteration for these Sinc–Galerkin systems is presented and it is shown that the two- Step Preconditioner is symmetric positive definite, and the condition number of the preconditionsed matrix is bounded by the convergence factor of the involved ADI iteration.

TL;DR: In this paper, the smooth LU decomposition of a given analytic functional and its block-analogue is studied, and sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided.

TL;DR: By making use of the Laplace transform, a class of two-stage waveform relaxation methods for solving the initial value problems of ordinary differential equations are presented, and sufficient conditions for guaranteeing their convergence when the system matrices are specifically H-matrices.

TL;DR: A class of parallel blockwise matrix multisplitting block relaxation methods is established for the large sparse block system of linear equations and its convergence theory is set up thorouthly when the coefficient matrix is a block H-matrix.

TL;DR: It is shown that the RHSS iteration method significantly outperforms the Hermitian and skew-Hermitian splitting iteration method in iteration counts and computing times when they are used either as linear iterative solvers or as matrix splitting preconditioners for Krylov subspace methods.