Copper Mountain Special Issue on Iterative Methods

Abstract

The biennial Copper Mountain Conference on Iterative Methods was held March 28-April 2, 2004, in Copper Mountain, Colorado. In addition to the traditional management services provided by Front Range Scientific Computations, Inc., Howard Elman (University of Maryland) and Panayot Vassilevski (Center for Applied Scientific Computing at LLNL) served as co-chairs representing the conference's new organizing institutions. The Conference gratefully acknowledges support from all three major national labs---Los Alamos, Lawrence Livermore, and Sandia---as well as support from the Department of Energy, IBM, and the National Science Foundation. Traditionally, the Copper Mountain Conference is organized in cooperation with the Society for Industrial and Applied Mathematics (SIAM). This special issue was open to the public and was advertised in advance on the web sites of both the SIAM Journal on Scientific Computing (SISC) and the Copper Mountain Conference. There were 35 manuscripts submitted; 15 found their place in this special issue. It is the guest editor-in-chief's opinion that these papers reflect state-of-the-art trends in iterative methods, among them parallel-block preconditioning, various improved versions of GMRES (block, relaxed, and flexible), approximate factorization preconditioners for saddle-point problems, and iterative methods exploiting deflation. But above all, this special issue clearly demonstrates the strong impact of multigrid/multilevel methods as the unique optimal-order iterative methods in various areas of applications. It also demonstrates the search for optimal-order methods or preconditioners on the basis of multilevel ideas in variety of nontraditional areas. I would like to thank the guest editorial board---Loyce Adams, Xiao-Chuan Cai, Iain Duff, Roland Freund, Anne Greenbaum, Tim Kelley, David Keyes, Tom Manteuffel, Steve McCormick, Ray Tuminaro, Henk van der Vorst, Olof Widlund, and Carol Woodward of the conference program committee---as well as Raymond Chan of the SISC editorial board and the many anonymous referees for their hard work to help meet the strict deadlines. I would also like to thank the SIAM staff for their constant support and efforts to bring this issue to life. Of course, this issue would not have been possible without the authors' contributions. Some of these submissions also appeared in the student paper competition, a unique event at the Copper Mountain conferences that has proven to be a very successful forum for presenting the latest results in the field. We have had increasingly strong participation from very talented recent Ph.D. holders and current Ph.D. students in this competition. We thank all the authors for their valuable contributions and hope that this special issue will stimulate further progress in this exciting area of research.