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 …

In many large scale scientific or engineering computations, ranging from computing the
frequency response of a circuit to the earthquake response of a buildingto the energy levels …

This book, Eigensystems, is the second volume in a projected five-volume series entitled
Matrix Algorithms. The first volume treated basic decompositions. The three following this …

This book, Basic Decompositions, is the first volume in a projected five-volume series
entitled Matrix Algorithms. The other four volumes will treat eigensystems, iterative methods …

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 …

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 …

Krylov subspace methods (KSMs) are iterative algorithms for solving large, sparse linear
systems and eigenvalue problems. Current KSMs rely on sparse matrix-vector multiply …

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 …

We have observed that the residual vectors at the end of each restart cycle of restarted
GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We …

Data communication within the memory system of a single processor node and between
multiple nodes in a system is the bottleneck in many iterative sparse matrix solvers like CG …