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 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 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 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
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
Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, this book contains all the material necessary for a graduate course on numerical linear algebra and numerous applications to engineering and science used in industry.
