Recent Advances in Iterative Methods

✍ Scribed by Dianne P. O’Leary (auth.), Gene Golub, Mitchell Luskin, Anne Greenbaum (eds.)

• Publisher: Springer-Verlag New York
• Year: 1994
• Tongue: English
• Leaves: 233
• Series: The IMA Volumes in Mathematics and its Applications 60
• Edition: 1
• Category: Library

✦ Synopsis

This IMA Volume in Mathematics and its Applications RECENT ADVANCES IN ITERATIVE METHODS is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra. " Large systems of matrix equations arise frequently in applications and they have the prop­ erty that they are sparse and/or structured. The purpose of this workshop was to bring together researchers in numerical analysis and various ap­ plication areas to discuss where such problems arise and possible meth­ ods of solution. The last two days of the meeting were a celebration dedicated to Gene Golub on the occasion of his sixtieth birthday, with the program arranged by Jack Dongarra and Paul van Dooren. We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Gene Golub, Anne Greenbaum, and Mitchell Luskin for organizing this workshop and editing the proceed­ ings. The financial support of the National Science Foundation and the Min­ nesota Supercomputer Institute made the workshop possible. A vner Friedman Willard Miller, Jr. xi PREFACE The solution of very large linear algebra problems is an integral part of many scientific computations.

✦ Table of Contents

Front Matter....Pages i-xvi
Some Themes in Gene H. Golub’s Work on Iterative Methods....Pages 1-11
Computing the Sparse Singular Value Decomposition via SVDPACK....Pages 13-29
Gaussian Quadrature Applied to Adaptive Chebyshev Iteration....Pages 31-44
Ordering Effects on Relaxation Methods Applied to the Discrete Convection-Diffusion Equation....Pages 45-57
On the Error Computation for Polynomial Based Iteration Methods....Pages 59-67
Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems....Pages 69-94
Matrices that Generate the same Krylov Residual Spaces....Pages 95-118
Incomplete Block Factorizations as Preconditioners for Sparse SPD Matrices....Pages 119-133
How Fast Can Iterative Methods Be....Pages 135-147
Rational Krylov Algorithms for Nonsymmetric Eigenvalue Problems....Pages 149-164
Highly Parallel Preconditioners for General Sparse Matrices....Pages 165-199
A Two-Stage Iteration for Solving Nearly Completely Decomposable Markov Chains....Pages 201-216
Minimum Residual Modifications to BI-CG and to the Preconditioner....Pages 217-225

✦ Subjects

Numerical Analysis