The Generating Function Method of Nonlinear Approximation

The generating function method is used to derive nonlinear approximations to a given function using any of a large variety of agreement conditions between function and approximation. The linear and fully nonlinear approximations coincide with Baker-Gammel approximants. While the latter exploits the...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 25; no. 1; pp. 235 - 244
Main Author Small, R. D.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.02.1988
Subjects
Approximation
Degrees of polynomials
Exact sciences and technology
Fourier series
Gaussian quadratures
Generating function
Mathematical functions
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Polynomials
Sciences and techniques of general use
Series convergence
Taylor series
Values
Non linear approximation
Approximation
Padé approximant
Generating function
Quadrature formula
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Summary:The generating function method is used to derive nonlinear approximations to a given function using any of a large variety of agreement conditions between function and approximation. The linear and fully nonlinear approximations coincide with Baker-Gammel approximants. While the latter exploits the correspondence between Pade approximants and Taylor series, the generating function method applies Newton-Cotes quadrature to the Stieltjes integral representation of the given function obtaining error terms from the quadrature errors
ISSN:0036-1429
1095-7170
DOI:10.1137/0725017