Numerical Linear Algebra with Applications book cover

Numerical Linear Algebra with Applications

Using MATLAB

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.

Audience

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.

Hardbound, 628 Pages

Published: September 2014

Imprint: Academic Press

ISBN: 978-0-12-394435-1

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

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