Introduction to Numerical Computations

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Introduction to Numerical Computations. Abstract: Introduction to Numerical Computations Content: Front Cover Introduction to Numerical Computations Copyright Page Dedication Table of Contens 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 Evaluation3.3 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 Numetical Integration-Gaussian Methods Suggestions for Further Reading Chapter 6. SYSTEMS OF LINEAR EQUATIONS. 6.1 Basic Concepts6.2 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.V 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 Methods8.3 Error Estimates 8.4 Practical Aspects of Solving Differential Equations 8.5 Boundary Value Problems Suggestions for Further Reading APPENDIX BIBLIOGRAPHY INDEX Computer Science and Applied Mathematics.