Huang Ting-zhu

PRECONDITIONED GAUSS-SEIDEL TYPE ITERATIVE METHOD FOR SOLVING LINEAR SYSTEMS ∗

The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed. Also the optimal parameter is presented. Numerical results show that the proper choice of the preconditioner can lead to effective by the preconditioned Gauss-Seidel type iterative methods for solving linear systems.

Block H-matrices and spectrum of block matrices

The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.

CONVERGENCE THEOREMS FOR THE AOR METHOD

Practical sufficient conditions for the convergence of the AOR method and a practical sufficient condition forH-matrices are studied. The obtained convergence conditions suited to matrices which need not to be diagonally dominant.

The stability of the linear systems with delays

In this paper, we study the linear autonomous system of differential difference equations with delays. Some simple and practical sufficient conditions of the hyperbolic cone and the asymptotic stable cone are established.