Introduction to Numerical Computations

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