NUMERICAL LINEAR ALGEBRA-------PHI
Description:
This well-organized text provides a clear analysis of the fundamental concepts of numerical linear algebra. It presents various numerical methods for the basic topics of linear algebra with a detailed discussion on theory, algorithms, and MATLAB implementation.
The book provides a review of matrix algebra and its important results in the opening chapter and examines these results in the subsequent chapters. With clear explanations, the book analyzes different kinds of numerical algorithms for solving linear algebra such as the elimination and iterative methods for linear systems, the condition number of a matrix, singular value decomposition (SVD) of a matrix, and linear least-squares problem. In addition, it describes the Householder and Givens matrices and their applications, and the basic numerical methods for solving the matrix eigenvalue problem. Finally, the text reviews the numerical methods for systems and control.
Key Features
Includes numerous worked-out examples to help students grasp the concepts easily.
Provides chapter-end exercises to enable students to check their comprehension of the topics discussed.
Gives answers to exercises with hints at the end of the book.
Uses MATLAB software for problem-solving.
Primarily designed as a textbook for postgraduate students of Mathematics, this book would also serve as a handbook on matrix computations for scientists and engineers.
Contents:
1. REVIEW OF MATRIX ALGEBRA
2. COMPUTER ARITHMETIC
3. VECTOR AND MATRIX NORMS
4. NUMERICAL STABILITY AND PROBLEM CONDITIONING
5. ELIMINATION METHODS FOR LINEAR SYSTEMS
6. ITERATIVE METHODS FOR LINEAR SYSTEMS
7. CONDITION NUMBER OF A MATRIX
8. SINGULAR VALUE DECOMPOSITION OF A MATRIX
9. LINEAR LEAST-SQUARES PROBLEM
10. HOUSEHOLDER MATRICES AND THEIR APPLICATIONS
11. GIVENS MATRICES AND THEIR APPLICATIONS
12. NUMERICAL METHODS FOR MATRIX EIGENVALUE PROBLEM
13. NUMERICAL METHODS FOR SYSTEMS AND CONTROL
Appendix
Bibliography
Answers with Hints to Problems
Index
