The development of ARPACK began as a research code written in Matlab and then in
Fortran 77 in 1990. Initially, the code was developed to study and verify the properties of the …

The Kronecker product has a rich and very pleasing algebra that supports a wide range of
fast, elegant, and practical algorithms. Several trends in scientific computing suggest that …

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 …

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 …

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 …

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 …

New restarted Lanczos bidiagonalization methods for the computation of a few of the largest
or smallest singular values of a large matrix are presented. Restarting is carried out by …

In this paper, we propose a restarted variant of the Lanczos method for symmetric
eigenvalue problems named the thick-restart Lanczos method. This new variant is able to …