Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems. Content: Front Matter, Page iii Copyright, Page iv Preface, Pages v-vi, David R. Kincaid, Linda J. Hayes Authors of Chapters, Pages vii-viii Papers Presented at Conference, Pages ix-xii,xiv Professor David M. Young, Jr., Pages xv-xxiv Chapter 1 - Fourier Analysis of Two–Level Hierarchical Basis Preconditioners, Pages 1-16, LOYCE M. ADAMS Chapter 2 - An Algebraic Framework for Hierarchical Basis Functions Multilevel Methods or the Search for ‘Optimal’ Preconditioners, Pages 17-40, OWE AXELSSON Chapter 3 - ELLPACK and ITPACK as Research Tools for Solving Elliptic Problems, Pages 41-63, GARRETT BIRKHOFF, ROBERT E. LYNCH Chapter 4 - Preconditioned Iterative Methods for Indefinite Symmetric Toeplitz Systems, Pages 65-79, PAUL CONCUS, PAUL E. SAYLOR Chapter 5 - A Local Relaxation Scheme (Ad-Hoc SOR) Applied to Nine Point and Block Difference Equations, Pages 81-90, L.W. EHRLICH Chapter 6 - Block Iterative Methods for Cyclically Reduced Non-Self-Adjoint Elliptic Problems, Pages 91-105, HOWARD C. ELMAN, GENE H. GOLUB Chapter 7 - Toward an Effective Two-Parameter SOR Method, Pages 107-119, GENE H. GOLUB, JOHN E. DE PILLIS Chapter 8 - Relaxation Parameters for the IQE Iterative Procedure for Solving Semi-Implicit Navier-Stokes Difference Equations, Pages 121-134, LOUIS A. HAGEMAN Chapter 9 - Hodie Approximation of Boundary Conditions, Pages 135-147, ROBERT E. LYNCH Chapter 10 - Iterative Methods for Nonsymmetric Linear Systems, Pages 149-171, WAYNE D. JOUBERT, THOMAS A. MANTEUFFEL Chapter 11 - Solution of Three-Dimensional Generalized Poisson Equations on Vector Computers, Pages 173-191, DAVID L. HARRAR II, JAMES M. ORTEGA Chapter 12 - Multi-Level Asynchronous Iteration for PDEs, Pages 193-213, D.C. MARINESCU, J.R. RICE Chapter 13 - An Adaptive Algorithm for Richardson's Method, Pages 215-233, PAUL E. SAYLOR Chapter 14 - A Note on the SSOR and USSOR Iterative Methods Applied to p-Cyclic Matrices, Pages 235-249, XIEZHANG LI, RICHARD S. VARGA Chapter 15 - The ADI Minimax Problem for Complex Spectra, Pages 251-271, EUGENE L. WACHSPRESS Chapter 16 - Some Domain Decomposition Algorithms for Elliptic Problems, Pages 273-291, MAKSYMILIAN DRYJA, OLOF B. WIDLUND Chapter 17 - The Search for Omega, Pages 293-311, DAVID M. YOUNG, TSUN-ZEE MAI Index, Pages 313-319 Edited By David R. Kincaid And Linda J. Hayes. Papers From A Conference Held Oct. 19-21, 1988, At The Center For Numerical Analysis Of The University Of Texas At Austin. Includes Bibliographical References.
