On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems

On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems

The solution of nonsymmetric systems of linear equations continues to be a diicult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s>0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choic...

GGMRES: A GMRES--type algorithm for solving singular linear equations with index one

In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

the block lsmr algorithm for solving linear systems with multiple right-hand sides

lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

Solving Shifted Linear Systems with Gmres and Applications to Lattice Gauge Theory Solving Shifted Linear Systems with Gmres and Applications to Lattice Gauge Theory 1. Introduction

of a matrix M 2 C nn and a vector r 2 C n are identical for all 2 C. This fact can be used in Krylov subspace iterative methods (where the