Copper Mountain Special Issue on Iterative Methods

Abstract

The Copper Mountain Conference on Iterative Methods, a biennial event organized by the University of Colorado in cooperation with SIAM, has become a tradition. The seventh edition took place March 24--29, 2002, and while traditions are often associated with graying hairs, the Copper Mountain keywords are still fresh, young, dynamic, and inspiring. It is the successful formula developed by Tom Manteuffel and Steve McCormick that keeps the event going strong. In publishing, one has to be prudent with traditions, but the formula led again in 2002 to an attractive mix of new, valuable material, and it was readily decided by the Program Committee to collect the best contributions as papers to form the kernel of a special issue. As in foregoing years, the committee members accepted the invitation to act as guest editors. SIAM accepted our proposal and offered us space in SISC. This special issue was well announced, even in advance of the conference, to offer those not attending the opportunity to contribute. In past years this open procedure had led to highly appreciated special issues. When the deadline for submission had expired, we found some 32 manuscripts on our desks, which after careful refereeing led to this eventual collection of 22 outstanding papers. (Some papers that failed to meet intermediate deadlines will find their way into regular issues of SISC.) These 22 papers reflect the best new ideas on various aspects of iterative methods, with continuing research efforts on preconditioning (seven manuscripts). The separation between multigrid and iterative techniques, once very strict, has become more vague, and so we find eight manuscripts that explore ideas based on the multigrid paradigm (including multilevel ideas). Iterative methods related to eigenproblems, an upcoming field in the 1990s, fell back to one or, with some goodwill, two papers. Personally I hope that this is a temporary dip. The other papers cover various ideas, such as improvements of the good old Gram--Schmidt orthogonalization procedure, inexact Newton methods, and continuation methods. The quality of this issue depends on the hard work and dedication of many people, among whom the authors are of course the most visible. We would like to thank the many anonymous referees for their hard work and their efforts to help meet the strict deadlines. We also thank the SIAM staff for their kind support and for all their efforts in editing and helping bring this issue to life. It is now up to the reader to discover the many jewels in this treasure box. We hope that this special issue will stimulate further progress in our exciting area of research.