Numerical Linear Algebra

ISBN-10: 0387341595
ISBN-13: 9780387341590
Edition: 2008
List price: $59.95 Buy it from $3.98
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Description: This book brings together linear algebra, numerical methods and an easy to use programming environment under Matlab (and Scilab). One of the key features of the book is the worked out examples and exercises at the end of each chapter. The reader is  More...

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Book details

List price: $59.95
Copyright year: 2008
Publisher: Springer
Publication date: 12/5/2007
Binding: Hardcover
Pages: 271
Size: 6.50" wide x 9.25" long x 0.75" tall
Weight: 1.144
Language: English

This book brings together linear algebra, numerical methods and an easy to use programming environment under Matlab (and Scilab). One of the key features of the book is the worked out examples and exercises at the end of each chapter. The reader is asked to do some numerical experiments in Matlab and then to prove the results theoretically. The book is a combination and update of two earlier French books by the authors. It is appropriate for both undergraduate and beginning graduate courses in mathematics as well as for working scientists and engineers as a self-study tool and reference.

Introduction
Discretization of a Differential Equation
Least Squares Fitting
Vibrations of a Mechanical System
The Vibrating String
Image Compression by the SVD Factorization
Definition and Properties of Matrices
Gram-Schmidt Orthonormalization Process
Matrices
Trace and Determinant
Special Matrices
Rows and Columns
Row and Column Permutation
Block Matrices
Spectral Theory of Matrices
Matrix Triangularization
Matrix Diagonalization
Min-Max Principle
Singular Values of a Matrix
Exercises
Matrix Norms, Sequences, and Series
Matrix Norms and Subordinate Norms
Subordinate Norms for Rectangular Matrices
Matrix Sequences and Series
Exercises
Introduction to Algorithmics
Algorithms and pseudolanguage
Operation Count and Complexity
The Strassen Algorithm
Equivalence of Operations
Exercises
Linear Systems
Square Linear Systems
Over- and Underdetermined Linear Systems
Numerical Solution
Floating-Point System
Matrix Conditioning
Conditioning of a Finite Difference Matrix
Approximation of the Condition Number
Preconditioning
Exercises
Direct Methods for Linear Systems
Gaussian Elimination Method
LU Decomposition Method
Practical Computation of the LU Factorization
Numerical Algorithm
Operation Count
The Case of Band Matrices
Cholesky Method
Practical Computation of the Cholesky Factorization
Numerical Algorithm
Operation Count
QR Factorization Method
Operation Count
Exercises
Least Squares Problems
Motivation
Main Results
Numerical Algorithms
Conditioning of Least Squares Problems
Normal Equation Method
QR Factorization Method
Householder Algorithm
Exercises
Simple Iterative Methods
General Setting
Jacobi, Gauss-Seidel, and Relaxation Methods
Jacobi Method
Gauss-Seidel Method
Successive Overrelaxation Method (SOR)
The Special Case of Tridiagonal Matrices
Discrete Laplacian
Programming Iterative Methods
Block Methods
Exercises
Conjugate Gradient Method
The Gradient Method
Geometric Interpretation
Some Ideas for Further Generalizations
Theoretical Definition of the Conjugate Gradient Method
Conjugate Gradient Algorithm
Numerical Algorithm
Number of Operations
Convergence Speed
Preconditioning
Chebyshev Polynomials
Exercises
Methods for Computing Eigenvalues
Generalities
Conditioning
Power Method
Jacobi Method
Givens-Householder Method
QR Method
Lanczos Method
Exercises
Solutions and Programs
Exercises of Chapter 2
Exercises of Chapter 3
Exercises of Chapter 4
Exercises of Chapter 5
Exercises of Chapter 6
Exercises of Chapter 7
Exercises of Chapter 8
Exercises of Chapter 9
Exercises of Chapter 10
References
Index
Index of Programs

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