Introduction to the Special Section on Sparse and Structured Matrices and Their Applications

Abstract

The field of sparse matrices is a broad and important area of the computational sciences that includes structured matrices and those with seemingly little or no structure. The relevance of the field is highlighted by the wide range of application areas that require the exploitation of matrix sparsity and structure in order to achieve a solution given real-world constraints on computing resources and/or time. Applications in which sparse matrices appear include structural analysis, computational fluid dynamics, economic modeling, financial analysis, numerical optimization, statistical modeling, power network analysis, electromagnetics, meteorology, medical imaging, data mining, and many more. A number of significant advancements in sparse matrix computations have been made in recent years. These advances have led to new challenges as multidisciplinary problems are now ambitiously posed, and they symbolize the growth in the area and demonstrate the dependence of the future of many fields on sparse matrix methods. Moreover, they give rise to a host of new problems that have yet to be addressed by the sparse matrix community. The Second SIAM Conference on Sparse Matrices, which was held in Coeur d'Alene, Idaho, October 9--11, 1996, was organized specifically to address some of the challenging issues in sparse matrix computations. This special issue of SIAM Journal on Matrix Analysis and Applications consists of some of the outstanding papers that were presented at the Sparse Matrix conference. Because of an error in scheduling, the paper titled ``Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method" by Richard Lehoucq, which should have appeared in this section, was published in SIAM Journal on Matrix Analysis and Applications, volume 20, number 1. We are grateful to Paul van Dooren, the Editor-in-Chief of SIAM Journal on Matrix Analysis and Applications, and the SIAM office for agreeing to publish a special section on sparse matrices. We would like to thank Roland Freund, Anne Greenbaum, Joseph Liu, and Zdenek Strakos for serving on the Guest Editorial Board; their effort and cooperation in handling the papers were much appreciated. Finally, we would like to express thanks to all the authors who have submitted papers to the special section; it would not have become a reality without their support.