Book description
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 realworld 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
Table of contents
 Cover image
 Title page
 Table of Contents
 Copyright
 Dedication
 List of Figures
 List of Algorithms
 Preface
 Chapter 1: Matrices
 Chapter 2: Linear Equations
 Chapter 3: Subspaces
 Chapter 4: Determinants
 Chapter 5: Eigenvalues and Eigenvectors
 Chapter 6: Orthogonal Vectors and Matrices
 Chapter 7: Vector and Matrix Norms
 Chapter 8: Floating Point Arithmetic
 Chapter 9: Algorithms

Chapter 10: Conditioning of Problems and Stability of Algorithms
 Abstract
 10.1 Why do we need numerical linear algebra?
 10.2 Computation error
 10.3 Algorithm stability
 10.4 Conditioning of a problem
 10.5 Perturbation analysis for solving a linear system
 10.6 Properties of the matrix condition number
 10.7 Matlab computation of a matrix condition number
 10.8 Estimating the condition number
 10.9 Introduction to perturbation analysis of eigenvalue problems
 10.10 Chapter summary
 10.11 Problems

Chapter 11: Gaussian Elimination and the LU Decomposition
 Abstract
 11.1 LU Decomposition
 11.2 Using LU to Solve Equations
 11.3 Elementary Row Matrices
 11.4 Derivation of the LU Decomposition
 11.5 Gaussian Elimination with Partial Pivoting
 11.6 Using the LU Decomposition to Solve Axi=bi,1≤i≤k
 11.7 Finding A–1
 11.8 Stability and Efficiency of Gaussian Elimination
 11.9 Iterative Refinement
 11.10 Chapter Summary
 11.11 Problems
 Chapter 12: Linear System Applications
 Chapter 13: Important Special Systems
 Chapter 14: GramSchmidt Orthonormalization
 Chapter 15: The Singular Value Decomposition
 Chapter 16: LeastSquares Problems

Chapter 17: Implementing the QR Decomposition
 Abstract
 17.1 Review of the QR Decomposition Using GramSchmidt
 17.2 Givens Rotations
 17.3 Creating a Sequence of Zeros in a Vector Using Givens Rotations
 17.4 Product of a Givens Matrix with a General Matrix
 17.5 ZeroingOut Column Entries in a Matrix Using Givens Rotations
 17.6 Accurate Computation of the Givens Parameters
 17.7 THe Givens Algorithm for the QR Decomposition
 17.8 Householder Reflections
 17.9 Computing the QR Decomposition Using Householder Reflections
 17.10 Chapter Summary
 17.11 Problems

Chapter 18: The Algebraic Eigenvalue Problem
 Abstract
 18.1 Applications of The Eigenvalue Problem
 18.2 Computation of Selected Eigenvalues and Eigenvectors
 18.3 The Basic QR Iteration
 18.4 Transformation to Upper Hessenberg Form
 18.5 The Unshifted Hessenberg QR Iteration
 18.6 The Shifted Hessenberg QR Iteration
 18.7 Schur's Triangularization
 18.8 The Francis Algorithm
 18.9 Computing Eigenvectors
 18.10 Computing Both Eigenvalues and Their Corresponding Eigenvectors
 18.11 Sensitivity of Eigenvalues to Perturbations
 18.12 Chapter Summary
 18.13 Problems
 Chapter 19: The Symmetric Eigenvalue Problem
 Chapter 20: Basic Iterative Methods

Chapter 21: Krylov Subspace Methods
 Abstract
 21.1 Large, Sparse Matrices
 21.2 The CG Method
 21.3 Preconditioning
 21.4 Preconditioning For CG
 21.5 Krylov Subspaces
 21.6 The Arnoldi Method
 21.7 GMRES
 21.8 The Symmetric Lanczos Method
 21.9 The Minres Method
 21.10 Comparison of Iterative Methods
 21.11 Poisson's Equation Revisited
 21.12 The Biharmonic Equation
 21.13 Chapter Summary
 21.14 Problems
 Chapter 22: Large Sparse Eigenvalue Problems
 Chapter 23: Computing the Singular Value Decomposition
 Appendix A: Complex Numbers
 Appendix B: Mathematical Induction
 Appendix C: Chebyshev Polynomials
 Glossary
 Bibliography
 Index
Product information
 Title: Numerical Linear Algebra with Applications
 Author(s):
 Release date: September 2014
 Publisher(s): Academic Press
 ISBN: 9780123947840
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