Many advances in the development of Krylov subspace methods for the iterative solution of
linear systems during the last decade and a half are reviewed. These new developments …

Many problems in science and engineering require the solution of a long sequence of slowly
changing linear systems. We propose and analyze two methods that significantly reduce the …

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

A modification is given of the GMRES iterative method for nonsymmetric systems of linear
equations. The new method deflates eigenvalues using Wu and Simon's thick restarting …

In this paper, a time-space fractional diffusion equation in two dimensions (TSFDE-2D) with
homogeneous Dirichlet boundary conditions is considered. The TSFDE-2D is obtained from …

Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal
basis for the entire Krylov subspace to compute the minimal residual approximation to the …

This survey concerns subspace recycling methods, a popular class of iterative methods that
enable effective reuse of subspace information in order to speed up convergence and find …

In this article we introduce new bounds on the effective condition number of deflated and
preconditioned-deflated symmetric positive definite linear systems. For the case of a …

The generalized minimum residual method (GMRES) is well known for solving large
nonsymmetric systems of linear equations. It generally uses restarting, which slows the …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …