Overview
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.
Full Product Details
Author: George A. Anastassiou ,
Sorin G. Gal
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: Softcover reprint of the original 1st ed. 2000
Dimensions:
Width: 15.50cm
, Height: 2.70cm
, Length: 23.50cm
Weight: 0.825kg
ISBN: 9781461271123
ISBN 10: 1461271126
Pages: 525
Publication Date: 08 October 2012
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
This monograph is an intensive and comprehensive study of the computational aspects of the moduli of smoothness and the Global Smoothness Preservation Property (GSPP). ---Zentralblatt MATH Going over the introduction, the reader will get an almost full account, without proofs, of the results presented in the monograph... There are many questions for further research arising from this interesting book. Some of them are formulated by the authors, but many more may be born in the mind of the reader. -Zentralblatt Math.
This monograph is an intensive and comprehensive study of the computational aspects of the moduli of smoothness and the Global Smoothness Preservation Property (GSPP). ---Zentralblatt MATH Going over the introduction, the reader will get an almost full account, without proofs, of the results presented in the monograph... There are many questions for further research arising from this interesting book. Some of them are formulated by the authors, but many more may be born in the mind of the reader. -Zentralblatt Math.
This monograph is an intensive and comprehensive study of the computational aspects of the moduli of smoothness and the Global Smoothness Preservation Property (GSPP). ---Zentralblatt MATH Going over the introduction, the reader will get an almost full account, without proofs, of the results presented in the monograph... There are many questions for further research arising from this interesting book. Some of them are formulated by the authors, but many more may be born in the mind of the reader. -Zentralblatt Math.
