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.