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Book Details

  New Book

Matrices, Moments and Quadrature with Applications


By GENE H. GOLUB (Author), GéRARD MEURANT (Author)
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Price : $99.95  $79.96
ISBN : 9780691143415  
Page : 376
Year of Publication : 2009    Edition : 1
Publisher : PRINCETON UNIVERSITY PRESS
Subject : MATHEMATICS & STATISTICS



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Description :

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.

Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization.

This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.



Gene H. Golub (1932-2007) was the Fletcher Jones Professor of Computer Science at Stanford University and the coauthor of Matrix Computations.Gérard Meurant, the author of three books on numerical linear algebra, has worked in scientific computing for almost four decades. He is retired from France's Commissariat à l'Énergie Atomique.

Content :

Preface

Part 1. Theory

Chapter 1. Introduction

Chapter 2. Orthogonal Polynomials

Chapter 3. Properties of Tridiagonal Matrices

Chapter 4. The Lanczos and Conjugate Gradient Algorithms

Chapter 5. Computation of the Jacobi Matrices

Chapter 6. Gauss Quadrature

Chapter 7. Bounds for Bilinear Forms

Chapter 8. Extensions to Nonsymmetric Matrices

Chapter 9. Solving Secular Equations

Applications

Chapter 10. Examples of Gauss Quadrature Rules

Chapter 11. Bounds and Estimates for Elements of Functions of Matrices

Chapter 12. Estimates of Norma of Errors in the Conjugate Gradient Algorithm

Chapter 13. Least Squares Problems

Chapter 14. Total Least Squares

Chapter 15. Discrete III-Posed Problems

Bibliography

Index

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