Numerical linear algebra with applications : using MATLAB

✍ Scribed by William Ford

• Publisher: Academic Press, , Elsevier Inc
• Year: 2014
• Tongue: English
• Leaves: 605
• Edition: 1
• Category: Library

✦ Synopsis

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.

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

✦ Table of Contents

Content:
Front Matter, Pages i-ii
Copyright, Page iv
Dedication, Page v
List of Figures, Pages xiii-xv
List of Algorithms, Page xvii
Preface, Pages xix-xxvi
Chapter 1 - Matrices, Pages 1-23
Chapter 2 - Linear Equations, Pages 25-45
Chapter 3 - Subspaces, Pages 47-58
Chapter 4 - Determinants, Pages 59-77
Chapter 5 - Eigenvalues and Eigenvectors, Pages 79-101
Chapter 6 - Orthogonal Vectors and Matrices, Pages 103-118
Chapter 7 - Vector and Matrix Norms, Pages 119-144
Chapter 8 - Floating Point Arithmetic, Pages 145-162
Chapter 9 - Algorithms, Pages 163-179
Chapter 10 - Conditioning of Problems and Stability of Algorithms, Pages 181-204
Chapter 11 - Gaussian Elimination and the LU Decomposition, Pages 205-239
Chapter 12 - Linear System Applications, Pages 241-262
Chapter 13 - Important Special Systems, Pages 263-280
Chapter 14 - Gram-Schmidt Orthonormalization, Pages 281-297
Chapter 15 - The Singular Value Decomposition, Pages 299-320
Chapter 16 - Least-Squares Problems, Pages 321-349
Chapter 17 - Implementing the QR Decomposition, Pages 351-378
Chapter 18 - The Algebraic Eigenvalue Problem, Pages 379-438
Chapter 19 - The Symmetric Eigenvalue Problem, Pages 439-468
Chapter 20 - Basic Iterative Methods, Pages 469-490
Chapter 21 - Krylov Subspace Methods, Pages 491-532
Chapter 22 - Large Sparse Eigenvalue Problems, Pages 533-549
Chapter 23 - Computing the Singular Value Decomposition, Pages 551-567
Appendix A - Complex Numbers, Pages 569-577
Appendix B - Mathematical Induction, Pages 579-581
Appendix C - Chebyshev Polynomials, Pages 583-585
Glossary, Pages 587-594
Bibliography, Pages 595-596
Index, Pages 597-602