Approximation Theory

Name: Approximation Theory
Brand: Springer-Verlag New York Inc.
SKU: 9781461271123
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Moduli of Continuity and Global Smoothness Preservation

Autor: George A. Anastassiou, Sorin G. Gal

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Oprawa: Miękka

Wydawca: Springer-Verlag New York Inc.

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We study in Part I of this monograph the computational aspect of almost all moduli of continuity ove...

Informacje o książce

Autor

George A. Anastassiou, Sorin G. Gal

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2012

strony

525

EAN

9781461271123

ISBN

1461271126

Enbook ID

06795094

Wydawca

Springer-Verlag New York Inc.

Waga

825

Wymiary

155 x 235 x 30

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We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

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Approximation Theory

Moduli of Continuity and Global Smoothness Preservation

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