Numerical Linear Algebra with Applications



  • William Ford, University of the Pacific, Stockton, California, USA

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science.

With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for those who want to learn to solve linear algebra problems, and offers a thorough explanation of the issues and methods for practical computing, using MATLAB as the vehicle for computation. The proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs.

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Graduate or advanced undergraduate students in engineering, science, and mathematics, professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica.


Book information

  • Published: September 2014
  • ISBN: 978-0-12-394435-1


"...this is a book that merits careful consideration as a possible text for a course in numerical linear algebra, particularly one stressing applications to engineering and other areas of science."--MAA Reviews, January 2, 2015

Table of Contents

1. Matrices
2. Linear equations
3. Subspaces
4. Determinants
5. Eigenvalues and eigenvectors
6. Orthogonal vectors and matrices
7. Vector and matrix norms
8. Floating point arithmetic
9. Algorithms
10. Conditioning of problems and stability of algorithms
11. Gaussian elimination and the LU decomposition
12. Linear system applications
13. Important special systems
14. Gram-Schmidt decomposition
15. The singular value decomposition
16. Least-squares problems
17. Implementing the QR factorization
18. The algebraic eigenvalue problem
19. The symmetric eigenvalue problem
20. Basic iterative methods
21. Krylov subspace methods
22. Large sparse eigenvalue problems
23. Computing the singular value decomposition
Appendix A. Complex numbers
Appendix B. Mathematical induction
Appendix C. Chebyshev polynomials