Templates for the Solution of Linear Systems by Richard Barrett
Templates for the Solution of Linear Systems - Table of Contents
- 1. Introduction to Iterative Linear Solvers
- 2. Iterative Methods (CG, GMRES, BiCGSTAB, QMR)
- 3. Preconditioners (ILU, Jacobi, SOR, Domain Decomposition)
- 4. Related Issues: Stopping Criteria & Parallelism
- 5. Remaining Topics and Implementation Details
- A. Obtaining and Installing the Software
- B. Overview of the BLAS (Basic Linear Algebra Subprograms)
- C. Glossary of Numerical Terms
- D. Flowchart of Iterative Methods and Decision Trees
What You Will Learn in Templates for the Solution of Linear Systems
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods by Richard Barrett et al. is an authoritative, highly practical reference guide published by SIAM that provides scientific computing researchers, engineers, and applied mathematicians with standardized algorithmic implementations for solving large-scale sparse linear systems. This comprehensive volume guides readers through stationary iterative methods, nonstationary Krylov subspace solvers (CG, GMRES, BiCGSTAB, QMR), domain decomposition preconditioners, stopping criteria selection, parallel implementation strategies, and BLAS integration with exceptional algorithmic precision and structural clarity.
Designed for computational scientists, software engineers, numerical analysts, and quantitative researchers, this foundational text bridges abstract iterative linear algebra theory directly with high-performance software implementation. Barrett and co-authors detail step-by-step pseudo-code algorithms, convergence monitoring techniques, matrix-vector product efficiency, and decision trees for algorithm selection based on matrix properties (symmetry, positive definiteness, non-Hermitian structure). Whether you are developing parallel iterative solvers, optimizing finite element simulations, or integrating sparse linear algebra libraries, this book offers an indispensable roadmap.
Recognized globally as a fundamental benchmark in computational science, it stands as one of the best reference handbooks for numerical linear algebra algorithms and iterative methods. By unifying pseudo-code implementations with practical preconditioning strategies, it serves as an essential tool for mastering iterative solvers and scientific computing routines with confidence.
Book Details & Specifications
Title:
Templates for the Solution of Linear Systems by Richard Barrett
Publisher:
Society for Industrial Mathematics
Year:
1987
Pages:
117
Type:
PDF
Language:
English
ISBN-10 #:
0898713285
ISBN-13 #:
9780898713282
License:
External Educational Resource
Amazon:
Amazon
About the Author: Richard Barrett
The author Richard Barrett
alongside co-authors Michael Berry, Tony F. Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk van der Vorst, represents an elite group of internationally renowned computer scientists and numerical analysts who pioneered modern high-performance computing, LAPACK/BLAS standards, and sparse linear algebra software frameworks.
Through Templates for the Solution of Linear Systems, this author collective delivers a clear, highly applicable algorithmic handbook. Their standardized pseudo-code formats, clear convergence guidance, and authoritative software flowcharts make this text a classic reference for iterative solver implementation and scientific software development trusted by engineers and researchers worldwide.
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