Applied Numerical Linear Algebra

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

James W. Demmel (Author)

9780898713893, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 August 1997

184 pages
25.4 x 17.2 x 1.9 cm, 0.856 kg

"Demmel's book covers the state of the art tools of numerical linear algebra. He tells us how they work and why they work so well. He also gives many references to recent research work. … he avoids including everything, so the book is still easy to read. …" -Martin H. Gutknecht, IPS Supercomputing in Zurich, Switzerland.

Designed for first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommending which algorithms to use in various practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in MATLAB and are freely available on the Web.

Preface
1. Introduction
2. Linear equation solving
3. Linear least squares problems
4. Nonsymmetric Eigenvalue problems
5. The symmetric Eigenproblem and singular value decomposition
6. Iterative methods for linear systems
7. Iterative methods for Eigenvalue problems
Bibliography
Index.

Subject Areas: Applied mathematics [PBW], Numerical analysis [PBKS], Algebra [PBF]