Copper Mountain Special Issue on Iterative Methods

Abstract

The 9th Copper Mountain Conference on Iterative Methods was held April 2–7, 2006, in Copper Mountain, Colorado. The conference is organized by Front Range Scientific Computations, Inc., with co-organizers the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory, and the University of Maryland. Traditionally, the SIAM Journal on Scientific Computing (SISC) hosts a special issue on iterative methods that is open to the public and is announced well in advance through both the SISC and the Copper Mountain Conference web sites. I would like to thank the current members of the program committee for their service as guest editorial board. The committee members are Xiao-Chuan Cai, University of Colorado; Iain Duff, RAL and CERFACS; Roland Freund, University of California, Davis; Kirk Jordan, IBM, Watson Research Center; Tim Kelley, North Carolina State University; David Keyes, Columbia University; Tom Manteuffel, University of Colorado; Steve McCormick, University of Colorado; David Silvester, University of Manchester; Ray Tuminaro, Sandia National Laboratory; Henk van der Vorst, University of Utrecht; Homer Walker, Worcester Polytechnic Institute; Carol Woodward, Lawrence Livermore National Laboratory; Irad Yavneh, Technion. The committee is chaired by Howard Elman (University of Maryland) and myself. This issue contains 21 papers that largely reflect the topics presented at the conference, including papers that were part of the student papers competition. More specifically, we have papers covering the more traditional numerical linear algebra topic of preconditioning, including preconditioners for nonsymmetric problems in GMRES, radial basis function interpolation via preconditioned Krylov iterations, preconditioned eigensolvers, graph-based algorithms for preconditioning, and strategies for constructing block preconditioners for systems of PDEs, as well as some emerging new topics, such as preconditioners for stochastic elliptic PDEs and linear systems arising in interior point optimization methods. Most of the papers deal with some aspects of iterative methods for systems of algebraic equations; however, a paper on iterative optimization procedures with application to image registration also found its place in the issue. The overwhelming majority of the papers deal with various aspects of (mostly algebraic) multigrid (or (A)MG), ranging from theory of geometric MG applied to nontraditional formulation of Stokes problems to investigation of a number of algorithmic issues in AMG (such as the construction of the interpolation operator, coarsening strategies including for nonsymmetric problems), as well as the construction of specialized AMG algorithms for Google PageRank-like problems and for problems arising from higher-order spectral elements discretizations. Many thanks are due to all authors for their valuable contributions. I would like also to thank the SIAM staff for their constant support and efforts to bring this issue to life. Finally, let me acknowledge the traditional support for the conference from the US Department of Energy, the National Science Foundation, IBM, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratory.