Some results on convergence of two-stage iterative methods for symmetric positive definite linear systems

Convergence on successive over-relaxed iterative methods for non-Hermitian positive definite linear systems

*Correspondence: [email protected] 1School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China Full list of author information is available at the end of the article Abstract Some convergence conditions on successive over-relaxed (SOR) iterative method and symmetric SOR (SSOR) iterative method are proposed for non-Hermitian positive definite linear systems. Some examples are ...

Convergence of Two-Stage Iterative Methods for Hermitian Positive Definite Matrices

Two-stage iterative methods for the solution of linear systems are studied. Convergence of both stationary and nonstationary cases is analyzed when the coefficient matrix is Hermitian positive definite. Keywords—Linear systems, Hermitian matrices, Positive definite matrices, Iterative methods, Nonstationary methods, Two-stage methods.

On Necessary Conditions for Convergence of Stationary Iterative Methods for Hermitian Definite and Semidefinite Linear Systems∗

In an earlier paper [SIAM J. Matrix Anal. Appl. vol. 30 (2008), 925–938] we gave sufficient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving singular linear systems whose coefficient matrix is Hermitian and positive semidefinite. In this paper we show in which cases these conditions are also necessary, and show that they are not necesary in othe...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

On the modified iterative methods for $M$-matrix linear systems

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...