| Approximation Theory: Moduli of Continuity and Global Smoothness Preservation 2000 Edition Contributor(s): Anastassiou, George A. (Author), Gal, Sorin G. (Author) |
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ISBN: 0817641513 ISBN-13: 9780817641511 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: December 1999 Annotation: This monograph, in two parts, is an intensive and comprehensive study of the computational aspects of the moduli of smoothness and the Global Smoothness Preservation Property (GSPP). Key features include: * systematic and extensive study of the computation of Moduli of Continuity and GSPP, presented for the first time in book form * substantial motivation and examples for key results * extensive applications of moduli of smoothness and GSPP concepts to approximation theory, probability theory, numerical and functional analysis * GSPP methods to benefit engineers in computer-aided geometric design * good bibliography and index For researchers and graduate students in pure and applied mathematics. |
| Additional Information |
| BISAC Categories: - Mathematics | Applied - Mathematics | Probability & Statistics - General - Mathematics | Mathematical Analysis |
| Dewey: 511.4 |
| LCCN: 99057004 |
| Physical Information: 1.2" H x 6.3" W x 9.38" (2.02 lbs) 525 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |