Convergence of block iterative methods for linear systems with generalized H-matrices

‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

Block Preconditioned SSOR Methods for H-Matrices Linear Systems

Received 9 January 2013; Accepted 12 March 2013 Academic Editor: Hak-Keung Lam Copyright © 2013 Z.-N. Pu and X.-Z. Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present a block preconditioner and consider block precondi...

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

Generalized Iterative Methods for augmented linear systems ∗

In this paper we study the solution of large sparse augmented linear systems. The generalized modified extrapolated SOR (GMESOR) method is considered. We find sufficient conditions for GMESOR to converge and determine its optimal iteration parameters and the corresponding minimum value of its convergence factor. Under the assumption that the eigenvalues of a key matrix are real it is shown that...

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...