In this review we discuss bifurcation theory in a Banach space setting using the singularity
theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical …

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 …

Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

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 …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

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 …

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 …

Eigenvalues and eigenfunctions of linear operators are important to many areas of applied
mathematics. The ability to approximate these quantities numerically is becoming …

This document describes slePc, the Scalable Library for Eigenvalue Problem Computations,
a software package for the solution of large sparse eigenproblems on parallel computers. It …

This goal of this paper is to present an elegant relationshipbetween an implicitly restarted
Arnoldi method (IRAM) and nonstationary (subspace) simultaneous iteration. This …