Special Issue on Iterative Methods for Solving Systems of Algebraic Equations

Abstract

This is the fourth in a series of special issues of SIAM Journal on Scientific Computing devoted to iterative methods for solving systems of algebraic equations. The results in these papers were originally presented at the Fifth Copper Mountain meeting on iterative methods, held in April 1998. There were 210 attendees at the conference and 135 presentations were made. This year's collection contains a very broad collection of topics. These include domain decomposition methods; a variety of preconditioning algorithms including approaches based on Fourier techniques, sparse approximate inverses of matrices, and multilevel methods; several innovative multigrid algorithms, including algebraic techniques and methods for nonlinear systems; special algorithms for nonlinear path following, accurate multipole computations in particle simulation, and deflation in the conjugate gradient method; application of techniques based on first order least squares in several applied settings (models of elasticity, scattering and subsurface flow); and spectral and convergence analysis of solution algorithms in electromagnetics. This is a reflection of the vibrancy of the field and the continued need for fast algorithms that match the accuracy requirements of practical models and are well suited to modern computer architectures. The papers in this volume were edited by an editorial board consisting of the following members of the Copper Mountain program committee: Iain Duff Roland Freund Anne Greenbaum Steve McCormick Seymour Parter Gerhard Starke Hank van der Vorst Homer Walker Olof Widlund I wish to thank them for their efforts in subjecting all submissions to a rigorous refereeing process. I also want to thank Tom Manteuffel and Steve McCormick, the organizers of the Copper Mountain conferences, for their work in making these meetings successful; with the multigrid meetings taking place on alternate years, there have now been fourteen such meetings held in Colorado. Special thanks are due to Fred Howes of the Department of Energy, Michael Steuerwalt of the National Science Foundation, Steve Ashby of Lawrence Livermore National Laboratory, and Kirk Jordan of IBM for generous support of the meeting. Finally, our deepest gratitude goes to Fred Howes, who was a consistent and strong supporter of these meetings and their goals. His untimely death represents a great loss to the community. This special issue is dedicated to his memory.