<scp>TriCG</scp> and <scp>TriMR</scp>: Two Iterative Methods for Symmetric Quasi-definite Systems

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...

Improvements of two preconditioned AOR iterative methods for Z-matrices

‎In this paper‎, ‎we propose two preconditioned AOR iterative methods to solve systems of linear equations whose coefficient matrices are Z-matrix‎. ‎These methods can be considered as improvements of two previously presented ones in the literature‎. ‎Finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

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...

Iterative Methods for the Partial Symmetric Eigenproblem

Robust Multilevel Methods for General Symmetric Positive Definite Operators

An abstract robust multilevel method for solving symmetric positive definite systems resulting from discretizing elliptic partial differential equations is developed. The term “robust” refers to the convergence rate of the method being independent of discretization parameters, i.e., the problem size, and problem parameters. Important instances of such problem parameters are in particular (highl...