Matrices, moments, and quadrature with applications / Gene H. Golub and Gerard Meurant.

Format:

Book

Author/Creator:

Golub, Gene H. (Gene Howard), 1932-2007.

Contributor:

Meurant, Gérard A.

Series:

Princeton series in applied mathematics.

Princeton series in applied mathematics

Language:

English

Subjects (All):

Matrices.

Numerical analysis.

Physical Description:

1 online resource (376 p.)

Edition:

Course Book

Place of Publication:

Princeton, N.J. : Princeton University Press, c2010.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

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 uTƒ(A)v

Chapter 8. Extensions to Nonsymmetric Matrices

Chapter 9. Solving Secular Equations

PART 2. Applications

Chapter 10. Examples of Gauss Quadrature Rules

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

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

Chapter 13. Least Squares Problems

Chapter 14. Total Least Squares

Chapter 15. Discrete Ill-Posed Problems

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 335-359) and index.

Description based on publisher supplied metadata and other sources.

ISBN:

9786612458019

9781282458017

1282458019

9781282936072

1282936077

9781400833887

1400833884

OCLC:

697182001