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 dissertation focuses on efficiently forming reduced-order models for large, linear
dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced …

In this paper we propose a new method for the iterative computation of a few of the extremal
eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based …

Sorensen's implicitly restarted Arnoldi algorithm is one of the most successful and flexible
methods for finding a few eigenpairs of a large matrix. However, the need to preserve the …

38 Davidson's method 115 39 Numerical example 116 40 Davidson's method and
preconditioning 119 41 The methods of Jacobi 120 42 The Jacobi-Davidson iteration …

This paper sketches the main research developments in the area of computational methods
for eigenvalue problems during the 20th century. The earliest of such methods dates back to …

The purpose of this book is to unify and document in one place many of the techniques and
much of the current understanding about solving systems of linear equations on vector and …