Numerical Linear Algebra with Applications: Using MATLAB

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book 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.

The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, 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.

This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to 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.

Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebraDetailed explanations and examplesA through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebraExamples from engineering and science applications

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