A Survey of Preconditioned Iterative Methods (Pitman Research Notes in Mathematics Series)

Are Magnus Bruaset

ISBN 10: 0582276543 / ISBN 13: 9780582276543

Published by Longman Scientific & Technical, 1995

About this Item

Paperback, xii + 162 pages. Limited gentle wear, a faint number on the upper outer page edges. Interior is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Straight spine. -- Solving large sparse linear systems from discretized partial differential equations requires efficient iterative methods; this book delivers a unified survey of preconditioned Krylov subspace techniques essential for researchers and practitioners in scientific computing. -- The text introduces iterative methods based on matrix splittings, covering classical techniques like Jacobi, Gauss-Seidel, and successive overrelaxation (SOR), as well as polynomial acceleration. It then develops the framework of Krylov subspace methods, deriving a generic algorithm that encompasses popular iterations such as the conjugate gradient (CG), GMRES, BICGSTAB, and QMR. Symmetric and nonsymmetric problems are addressed separately, with discussions on termination procedures and implementation efficiency. Preconditioning strategies form a central theme, including incomplete factorizations, approximate inverses, and polynomial preconditioners. The book also bridges algebraic tools with problem-oriented approaches like multigrid and domain decomposition, crucial for elliptic boundary value problems. -- This work offers a balanced blend of theoretical foundations, algorithmic details, and practical considerations, providing a durable framework for understanding solver performance. Its systematic treatment of preconditioning makes it an ideal resource for building robust simulation codes, calibrating models, and selecting optimal solution strategies for large-scale computations. It serves as both a concise learning guide and a conceptual reference for the mathematical underpinnings of modern iterative solvers.

Seller Inventory # 012069

Bibliographic Details

• Title: A Survey of Preconditioned Iterative Methods (Pitman Research Notes in Mathematics Series)
• Publisher: Longman Scientific & Technical
• Publication Date: 1995
• Language: English
• ISBN 10: 0582276543
• ISBN 13: 9780582276543
• Binding: Soft cover
• Edition: 1st Edition
• Condition: Good

About this title

Synopsis

The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are well suited for the kind of systems arising from the discretization of partial differential equations. The focus of this presentation is on the family of Krylov subspace solvers, of which the Conjugate Gradient algorithm is a typical example. In addition to an introduction to the basic principles of such methods, a large number of specific algorithms for symmetric and nonsymmetric problems are discussed. When solving linear systems by iteration, a preconditioner is usually introduced in order to speed up convergence. In many cases, the selection of a proper preconditioner is crucial to the resulting computational performance. For this reason, this book pays special attention to different preconditioning strategies. Although aimed at a wide audience, the presentation assumes that the reader has basic knowledge of linear algebra, and to some extent, of partial differential equations. The comprehensive bibliography in this survey is provides an entry point to the enormous amount of published research in the field of iterative methods.

About the Author

Are Magnus Bruaset