Introduction to Numerical Computations

Introduction to Numerical Computations

2nd Edition - May 28, 1983

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  • Author: James S. Vandergraft
  • eBook ISBN: 9781483267098

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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


    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




Product details

  • No. of pages: 388
  • Language: English
  • Copyright: © Academic Press 1983
  • Published: May 28, 1983
  • Imprint: Academic Press
  • eBook ISBN: 9781483267098

About the Author

James S. Vandergraft

About the Editor

Werner Rheinboldt

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