Applied Numerical Linear Algebra

  • 10h 22m
  • James W. Demmel
  • Society for Industrial and Applied Math
  • 1997

Designed for use by 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 recommendations of which algorithms to use in a variety of practical situations.

If you are looking for a textbook that - teaches state-of-the-art techniques for solving linear algebra problems, - covers the most important methods for dense and sparse problems, - presents both the mathematical background and good software techniques, - is self-contained, assuming only a good undergraduate background in linear algebra, then this is the book for you.

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.

In this Book

  • Introduction
  • Linear Equation Solving
  • Linear Least Squares Problems
  • Nonsymmetric Eigenvalue Problems
  • The Symmetric Eigenproblem and Singular Value Decomposition
  • Iterative Methods for Linear Systems
  • Iterative Methods for Eigenvalue Problems
  • Bibliography