Introduction to Numerical Computations - 2nd Edition - ISBN: 9780127113562, 9781483267098

Introduction to Numerical Computations

2nd Edition

Authors: James S. Vandergraft
Editors: Werner Rheinboldt
eBook ISBN: 9781483267098
Imprint: Academic Press
Published Date: 28th May 1983
Page Count: 388
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Description

Computer Science and Applied Mathematics: Introduction to Numerical Computations, Second Edition introduces numerical algorithms as they are used in practice.

This edition covers the usual topics contained in introductory numerical analysis textbooks that include all of the well-known and most frequently used algorithms for interpolation and approximation, numerical differentiation and integration, solution of linear systems and nonlinear equations, and solving ordinary differential equations. A complete discussion of computer arithmetic, problems that arise in the computer evaluation of functions, and cubic spline interpolation are also provided. This text likewise discusses the Newton formulas for interpolation and adaptive methods for integration.

The level of this book is suitable for advanced undergraduate students and readers with elementary mathematical background.

Table of Contents


Preface

Acknowledgments

List of Special Symbols

Chapter 1 Basic Aspects of Numerical Computations

1.1 Numerical Algorithms

1.2 Unstable Problems (Ill-Conditioning)

1.3 Unstable Methods

Suggestions for Further Reading

Chapter 2 Computer Arithmetic

2.1 Number Representation

2.2 Floating Point Numbers

2.3 Arithmetic Operations

2.4 Errors in Computer Arithmetic

2.5 Analysis of Errors

Suggestions for Further Reading

Chapter 3 Evaluation of Functions

3.1 Summation

3.2 Polynomial Evaluation

3.3 Rational and Transcendental Functions

3.4 Avoiding Subtractive Cancellation

Suggestions for Further Reading

Chapter 4 Interpolation and Approximation

4.1 Polynomial Interpolation

4.2 Least Squares Approximation

4.3 Spline Interpolation

Suggestions for Further Reading

Chapter 5 Differentiation and Integration

5.1 Numerical Differentiation

5.2 Numerical Integration—Newton-Cotes Formulas

5.3 Adaptive Integration

5.4 Romberg Integration

5.5 Numerical Integration—Gaussian Methods

Suggestions for Further Reading

Chapter 6 Systems of Linear Equations

6.1 Basic Concepts

6.2 Gaussian Elimination

6.3 Matrix Applications of Gaussian Elimination

6.4 Rounding Error Analysis

6.5 Error Estimates and Accuracy Improvement

6.6 Efficiency Estimates

6.7 Error Estimates—Matrix Methods

6.8 Iterative Methods

Suggestions for Further Reading

Chapter 7 Nonlinear Equations

7.1 Basic Methods

7.2 Convergence Results

7.3 Stability and Effects of Rounding Errors

7.4 Efficiency—Rates of Convergence

7.5 Roots of Polynomials

Suggestions for Further Reading

Chapter 8 Ordinary Differential Equations

8.1 Differential and Difference Equations

8.2 Basic Methods

8.3 Error Estimates

8.4 Practical Aspects of Solving Differential Equations

8.5 Boundary Value Problems

Suggestions for Further Reading

Appendix

Bibliography

Index

Details

No. of pages:
388
Language:
English
Copyright:
© Academic Press 1983
Published:
Imprint:
Academic Press
eBook ISBN:
9781483267098

About the Author

James S. Vandergraft

About the Editor

Werner Rheinboldt

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