Theoretical Numerical Analysis - 1st Edition - ISBN: 9781483233123, 9781483275222

Theoretical Numerical Analysis

1st Edition

Authors: Burton Wendroff
eBook ISBN: 9781483275222
Imprint: Academic Press
Published Date: 1st January 1966
Page Count: 252
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Description

Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics.

The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation.

The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems.

The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

Table of Contents


Preface

Preliminaries

Chapter 1. Interpolation and Quadrature

1.1. Hermite Interpolation

1.2. Lagrange Interpolation and Newton-Cotes Quadrature

1.3. Orthogonal Polynomials and Gaussian Quadrature

1.4. Nonanalytic Interpolation and Associated Quadrature

Exercises

Computer Problems

Notes

Chapter 2. Approximation

2.1. Degree of Approximation by Polynomials

2.2. Approximation by Interpolation

2.3. Chebyshev Approximation

2.4. An Algorithm for Chebyshev Approximation

Appendix

Exercises

Computer Problems

Notes

Chapter 3. Ordinary Differential Equations

3.1. The Initial Value Problem

3.2. An Inhomogeneous Boundary Value Problem

3.3. A Homogeneous Boundary Value Problem

Exercises

Computer Problems

Notes

Chapter 4. Solution of Equations

4.1. Matrix Inversion by Triangular Decomposition

4.2. The Matrix Eigenvalue Problem

4.3. Linear Iterative Methods

4.4. Iterative Methods for Nonlinear Systems

Exercises

Computer Problem

Notes

Chapter 5. Partial Differential Equations

5.1. First Order Systems

5.2. The Heat Equation

5.3. Stability

5.4. The Maximum Principle

Exercises

Notes

References

Additional Reading

Author Index

Subject Index

Details

No. of pages:
252
Language:
English
Copyright:
© Academic Press 1966
Published:
Imprint:
Academic Press
eBook ISBN:
9781483275222

About the Author

Burton Wendroff

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