Theory and applications of numerical analysis
Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis.The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program th...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
London ; New York ; Tokyo
Academic Press
1996
Elsevier Science & Technology |
| Edition | 2 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9780125535601 0125535600 |
Cover
Table of Contents:
- 13.12 Systems and higher order equations -- 13.13 Comparison of step-by-step methods -- Problems -- Chapter 14. Boundary value and other methods for ordinary differential equations -- 14.1 Shooting method for boundary value problems -- 14.2 Boundary value method -- 14.3 Extrapolation to the limit -- 14.4 Deferred correction -- 14.5 Chebyshev series method -- Problems -- Appendix: Computer arithmetic -- A.1 Binary numbers -- A.2 Integers and fixed point fractions -- A.3 Floating point arithmetic -- Problems -- Solutions to selected problems -- References and further reading -- Index
- 7.7 Numerical differentiation -- 7.8 Effect of errors -- Problems -- Chapter 8. Solution of algebraic equations of one variable -- 8.1 Introduction -- 8.2 The bisection method -- 8.3 Interpolation methods -- 8.4 One-point iterative methods -- 8.5 Faster convergence -- 8.6 Higher order processes -- 8.7 The contraction mapping theorem -- Problems -- Chapter 9. Linear equations -- 9.1 Introduction -- 9.2 Matrices -- 9.3 Linear equations -- 9.4 Pivoting -- 9.5 Analysis of elimination method -- 9.6 Matrix factorization -- 9.7 Compact elimination methods -- 9.8 Symmetric matrices -- 9.9 Tridiagonal matrices -- 9.10 Rounding errors in solving linear equations -- Problems -- Chapter 10. Matrix norms and applications -- 10.1 Determinants, eigenvalues and eigenvectors -- 10.2 Vector norms -- 10.3 Matrix norms -- 10.4 Conditioning -- 10.5 Iterative correction from residual vectors -- 10.6 Iterative methods -- Problems -- Chapter 11. Matrix eigenvalues and eigenvectors -- 11.1 Relations between matrix norms and eigenvalues -- Gerschgorin theorems -- 11.2 Simple and inverse iterative method -- 11.3 Sturm sequence method -- 11.4 The QR algorithm -- 11.5 Reduction to tridiagonal form: Householder's method -- Problems -- Chapter 12. Systems of non-linear equations -- 12.1 Contraction mapping theorem -- 12.2 Newton's method -- Problems -- 13. Ordinary differential equations -- 13.1 Introduction -- 13.2 Difference equations and inequalities -- 13.3 One-step methods -- 13.4 Truncation errors of one-step methods -- 13.5 Convergence of one-step methods -- 13.6 Effect of rounding errors on one-step methods -- 13.7 Methods based on numerical integration -- explicit methods -- 13.8 Methods based on numerical integration -- implicit methods -- 13.9 Iterating with the corrector -- 13.10 Milne's method of estimating truncation errors -- 13.11 Numerical stability
- Front Cover -- Theory and Applications of Numerical Analysis -- Copyright Page -- Contents -- Preface -- From the preface to the first edition -- Chapter 1. Introduction -- 1.1 What is numerical analysis? -- 1.2 Numerical algorithms -- 1.3 Properly posed and well-conditioned problems -- Problems -- Chapter 2. Basic analysis -- 2.1 Functions -- 2.2 Limits and derivatives -- 2.3 Sequences and series -- 2.4 Integration -- 2.5 Logarithmic and exponential functions -- Problems -- Chapter 3. Taylor's polynomial and series -- 3.1 Function approximation -- 3.2 Taylor's theorem -- 3.3 Convergence of Taylor series -- 3.4 Taylor series in two variables -- 3.5 Power series -- Problems -- Chapter 4. The interpolating polynomial -- 4.1 Linear interpolation -- 4.2 Polynomial interpolation -- 4.3 Accuracy of interpolation -- 4.4 The Neville-Aitken algorithm -- 4.5 Inverse interpolation -- 4.6 Divided differences -- 4.7 Equally spaced points -- 4.8 Derivatives and differences -- 4.9 Effect of rounding error -- 4.10 Choice of interpolating points -- 4.11 Examples of Bemstein and Runge -- Problems -- Chapter 5. 'Best' approximation -- 5.1 Norms of functions -- 5.2 Best approximations -- 5.3 Least squares approximation -- 5.4 Orthogonal functions -- 5.5 Orthogonal polynomials -- 5.6 Minimax approximation -- 5.7 Chebyshev series -- 5.8 Economization of power series -- 5.9 The Remez algorithms -- 5.10 Further results on minimax approximation -- Problems -- Chapter 6. Splines and other approximations -- 6.1 Introduction -- 6.2 B-splines -- 6.3 Equally spaced knots -- 6.4 Hermite interpolation -- 6.5 Padé and rational approximation -- Problems -- Chapter 7. Numerical integration and differentiation -- 7.1 Numerical integration -- 7.2 Romberg integration -- 7.3 Gaussian integration -- 7.4 Indefinite integrals -- 7.5 Improper integrals -- 7.6 Multiple integrals