Interpolation and Approximation by Rational Functions in the Complex Domain

Interpolation and Approximation by Rational Functions in the Complex Domain PDF Author: J. L. Walsh
Publisher: American Mathematical Soc.
ISBN: 0821810200
Category : Mathematics
Languages : en
Pages : 418

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Book Description
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Interpolation and Approximation by Rational Functions in the Complex Domain

Interpolation and Approximation by Rational Functions in the Complex Domain PDF Author: J. L. Walsh
Publisher: American Mathematical Soc.
ISBN: 0821810200
Category : Mathematics
Languages : en
Pages : 418

Get Book Here

Book Description
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Interpolation and Approximation by Rational Functions in the Complex Domain

Interpolation and Approximation by Rational Functions in the Complex Domain PDF Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 426

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Book Description


Rational Approximation and Interpolation

Rational Approximation and Interpolation PDF Author: P.R. Graves-Morris
Publisher: Springer
ISBN: 3540391134
Category : Mathematics
Languages : en
Pages : 541

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Book Description


Interpolation and Approximation

Interpolation and Approximation PDF Author: Philip J. Davis
Publisher: Courier Corporation
ISBN: 0486624951
Category : Mathematics
Languages : en
Pages : 418

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Book Description
Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.

 PDF Author:
Publisher: Springer Nature
ISBN: 3031651332
Category :
Languages : en
Pages : 598

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Book Description


Approximation by Bounded Analytic Functions

Approximation by Bounded Analytic Functions PDF Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Hardy spaces
Languages : en
Pages : 172

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Book Description


Walter Gautschi, Volume 1

Walter Gautschi, Volume 1 PDF Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 146147034X
Category : Mathematics
Languages : en
Pages : 700

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Book Description
Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

Bounded Analytic Functions

Bounded Analytic Functions PDF Author:
Publisher: Academic Press
ISBN: 0080874126
Category : Mathematics
Languages : en
Pages : 487

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Book Description
Bounded Analytic Functions

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability PDF Author: Jerzy Neyman
Publisher: Univ of California Press
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 652

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Book Description


Spline Functions: Basic Theory

Spline Functions: Basic Theory PDF Author: Larry Schumaker
Publisher: Cambridge University Press
ISBN: 1139463438
Category : Mathematics
Languages : en
Pages : 524

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Book Description
This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.