β Scribed by Rheinboldt, Werner; Vandergraft, James S
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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.
Numerical analysis.;MATHEMATICS -- Applied.;MATHEMATICS -- Probability & Statistics -- General.
π SIMILAR VOLUMES
Introduction to Numerical Computations (Computer Science & Applied Mathematics Monograph)
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