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A Simple Introduction to Numerical Analysis Volume 2: Interpolation and Approximation: A Computer Illustrated Text - Brossura
Sinossi
Approximation techniques are widely used in mathematics and applied physics, as exact solutions are frequently impossible to obtain. A Simple Introduction to Numerical Analysis, Volume 2: Interpolation and Approximation extends the first volume to consider problems in interpolation and approximation. Topics covered include the construction of interpolating functions, the determination of polynomial and rational function approximations, numerical quadrature, and the solution of boundary value problems in ordinary differential equations. As with the previous volume, the text is integrated with a software package that allows the reader to work through numerous examples. It is also possible to use the software to consider problems that are beyond the scope of the text. The authors' expertise in combining text and software has resulted in a very readable work.
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Contenuti
GETTING STARTED
Introduction
The software: an example
The software: general remarks
Screen dumps
Final remarks
INTERPOLATION
Polynomial interpolation
Lagrangian polynomials
Divided differences
Neville's algorithm
Spline interpolation
Summary and conclusion
THE APPROXIMATION OF FUNCTIONS
Taylor series approximation
Polynomial approximation
Minimax polynomials
Chebyshev approximation
Orthogonal functions
Fourier series expansions
Rational approximation
Applications and conclusions
LEAST SQUARES APPROXIMATION
Introduction
Linear least squares
Continuous least squares approximation
Discrete least squares approximation
INTEGRATION
Simple quadrature
Newton-Cotes methods
Gauss quadrature formulae
Composite quadrature
Romberg integration
Adaptive integration
The Clenshaw-Curtis method
DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS
Introduction
Solution in series
Finite element methods
Non-linear problems
APPENDICES
Mathematical background
Finite difference approximations
INDEX
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