This book is a friendly treatment of numerical linear algebra tailored to first-year graduate students from a variety of engineering and scientific disciplines. The treatment of rounding error analysis and perturbation theory is exceptionally thorough and careful.... The author's writing style is very clear and a pleasure to read.
—— William W. Hager, Mathematical Reviews, Issue 98m.
Compare Demmel with the standard work by G. Golub and C. Van Loan, Matrix Computations (3rd ed., 1996)... Demmel offers a smaller number of topics but focuses on the most important, and provides o more readable introduction for beginners.
—— B. Borchers, CHOICE, Vol. 35, No. 7, March 1998.
The disposition is very much like a series of lectures, new concepts ore introduced precisely where needed...Illustrating examples are given, some reporting really heavy computations, but the author does not shy away from giving mathematical proofs where that is needed...
—— A. Ruhe, Zeitschrift f?r Mathematik und ihre Grenzgebiete, Band 879/98.
If you do any computing with matrices—— including linear systems, least squares and eigenvolues—— this book cannot but help you understand what you are doing and why. It presents state-of-the art material (as of June 1997) and can serve as a text or a reference...
—— L. Ehrlich, Computing Reviews, February 1998.
2im Demmel's book on applied numerical linear algebra is a wonderful text blending together the mathematical basis, good numerical software, and practical knowledge for solving real problems. It is destined to be o classic.
—— Jack Dongarra, University of Tennessee, Knoxville.
This is on excellent graduate-level textbook for people who want to learn or teach the state of the art of numerical linear algebra. It covers systematically all the fundamental topics in theory, as well as software implementation. The book is very easy to use in the classroom since it provides pointers, in the book and the author's home page, to lots of available Matlab and LAPACK routines, and it has a large number of homework problems marked Easy, Medium, and Hard. The book requires the students to have a stronger background in linear algebra than most other engineering books on numerical linear algebra.
—— Xia-Chuan Cai, University Of Colorado.
1.1 Basic Notation
1.2 Standard Problems of Numerical Linear Algebra
1.3 General Techniques
1.3.1 Matrix Factorizations
1.3.2 Perturbation Theory and Condition Numbers
1.3.3 Effects of Roundoff Error on Algorithms
1.3.4 Analyzing the Speed of Algorithms
1.3.5 Engineering Numerical Software
1.4 Example: Polynomial Evaluation
1.5 Floating Point Arithmetic
1.5.1 Further Details
1.6 Polynomial Evaluation Revisited
1.7 Vector and Matrix Norms
1.8 References and Other Topics for Chapter 1
1.9 Questions for Chapter 1
2 Linear Equation Solving
2.2 Perturbation Theory
2.2.1 Relative Perturbation Theory
2.3 Gaussian Elimination
2.4 Error Analysis
2.4.1 The Need for Pivoting
2.4.2 Formal Error Analysis of Gaussian Elimination
2.4.3 Estimating Condition Numbers
2.4.4 Practical Error Bounds
2.5 Improving the Accuracy of a Solution
2.5.1 Single Precision Iterative Refinement
2.6 Blocking Algorithms for Higher Performance
2.6.1 Basic Linear Algebra Subroutines (BLAS)
2.6.2 How to Optimize Matrix Multiplication
2.6.3 Reorganizing Gaussian Elimination to Use Level 3 BLAS
2.6.4 More About Parallelism and Other Performance Issues.
2.7 Special Linear Systems
2.7.1 Real Symmetric Positive Definite Matrices
2.7.2 Symmetric Indefinite Matrices
2.7.3 Band Matrices
2.7.4 General Sparse Matrices
2.7.5 Dense Matrices Depending on Fewer Than O(n2) Parameters
2.8 References and Other Topics for Chapter 2
2.9 Questions for Chapter 2
3 Linear Least Squares Problems
3.2 Matrix Factorizations That Solve the Linear Least Squares Problem
3.2.1 Normal Equations
3.2.2 QR Decomposition
3.2.3 Singular Value Decomposition
3.3 Perturbation Theory for the Least Squares Problem
3.4 Orthogonal Matrices
3.4.1 Householder Transformations
3.4.2 Givens Rotations
3.4.3 Roundoff Error Analysis for Orthogonal Matrices
3.4.4 Why Orthogonal Matrices?
3.5 Rank-Deficient Least Squares Problems
3.5.1 Solving Rank-Deficient Least Squares Problems Using the SVD
3.5.2 Solving Rank-Deficient Least Squares Problems Using QR with Pivoting
3.6 Performance Comparison of Methods for Solving Least SquaresProblems
3.7 References and Other Topics for Chapter 3
3.8 Questions for Chapter 3
4 Nonsymmetric Eigenvalue Problems
4.2 Canonical Forms
4.2.1 Computing Eigenvectors from the Schur Form
4.3 Perturbation Theory
4.4 Algorithms for the Nonsymmetric Eigenproblem
4.4.1 Power Method
4.4.2 Inverse Iteration
4.4.3 Orthogonal Iteration
4.4.4 QR Iteration
4.4.5 Making QR Iteration Practical
4.4.6 Hessenberg Reduction