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Introduction to Numerical Computations
2nd Edition - May 28, 1983
Author: James S. Vandergraft
Editor: Werner Rheinboldt
eBook ISBN:9781483267098
9 7 8 - 1 - 4 8 3 2 - 6 7 0 9 - 8
Computer Science and Applied Mathematics: Introduction to Numerical Computations, Second Edition introduces numerical algorithms as they are used in practice. This edition covers… Read more
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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.
PrefaceAcknowledgmentsList of Special SymbolsChapter 1 Basic Aspects of Numerical Computations 1.1 Numerical Algorithms 1.2 Unstable Problems (Ill-Conditioning) 1.3 Unstable Methods Suggestions for Further ReadingChapter 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 ReadingChapter 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 ReadingChapter 4 Interpolation and Approximation 4.1 Polynomial Interpolation 4.2 Least Squares Approximation 4.3 Spline Interpolation Suggestions for Further ReadingChapter 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 ReadingChapter 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 ReadingChapter 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 ReadingChapter 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 ReadingAppendixBibliographyIndex
No. of pages: 388
Language: English
Edition: 2
Published: May 28, 1983
Imprint: Academic Press
eBook ISBN: 9781483267098
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