An Introduction to Numerical Mathematics - 1st Edition - ISBN: 9781483200385, 9781483225418

An Introduction to Numerical Mathematics

1st Edition

Authors: Eduard L. Stiefel
eBook ISBN: 9781483225418
Imprint: Academic Press
Published Date: 1st January 1963
Page Count: 296
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An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations.

Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table.

This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.

Table of Contents

Foreword to German Edition

Foreword to English Edition

Chapter I Linear Algebra

1.1 Linear Functions, Exchange

1.2 Inversion

1.3 Practical Solution of Linear Equations

Chapter 2 Linear Programming

2.1 An Introductory Example

2.2 Solution of a Program with the Exchange Method

2.3 Geometric Interpretation of the Simplex Algorithm

2.4 Generalizations

2.5 Method of Dual Solution

2.6 Application to Game Theory

2.7 Chebyshev Approximation

Chapter 3 Least-Squares Approximation and Definite Problems

3.1 The Method of Least-Squares

3.2 Definite Problems

3.3 Solution of Symmetric-Definite Equations

3.4 Orthogonality

Chapter 4 Nonlinear Algebra

4.1 Linearization

4.2 The Correction Method of Newton

4.3 Recursion formulas, Convergence

4.4 Newton's Method for Several Unknowns

4.5 Polynomials

4.6 Direct Methods for the Solution of Algebraic Equations

Chapter 5 Eigenvalue Problems

5.1 An Introductory Example

5.2 The Characteristic Polynomial

5.3 General Eigenvalue Problem, Iterative Methods

5.4 Outlooks

Chapter 6 Differential Equations

6.1 Numerical Differentiation

6.2 Numerical Integration

6.3 Differential Equations of the First Order

6.4 Systems of Differential Equations of the First Order

6.5 Boundary-Value Problems

6.6 Partial Differential Equations

Chapter 7 Approximations

7.1 The Interpolating Polynomial

7.2 Systems of Polynomials

7.3 Interpolation Problems in the Complex Plane

Appendix I. Computational Examples

Appendix II. Tables


Additional Literature-References in English

Author Index

Subject Index


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© Academic Press 1963
Academic Press
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About the Author

Eduard L. Stiefel

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