UID:
almahu_9947367215902882
Umfang:
1 online resource (461 p.)
Ausgabe:
2nd ed.
ISBN:
1-281-05438-0
,
9786611054380
,
0-08-051912-1
Inhalt:
This text 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 and the algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions
Anmerkung:
Description based upon print version of record.
,
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
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3.4 Taylor series in two variables3.5 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
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5.5 Orthogonal polynomials5.6 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
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7.7 Numerical differentiation7.8 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
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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
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Chapter 12. Systems of non-linear equations
,
English
Weitere Ausg.:
ISBN 0-12-553560-0
Sprache:
Englisch
