Overview
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Similar content being viewed by others
Table of contents (20 chapters)
-
Front Matter
-
Introduction
-
Calculus of the Moduli of Smoothness in Classes of Functions
-
Front Matter
-
-
Global Smoothness Preservation by Linear Operators
-
Front Matter
-
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.
Authors and Affiliations
Accessibility Information
PDF accessibility summary
This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or descriptions for non-text content (e.g., images and graphs). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at through this accessibility request webform if you require assistance or an alternative format.
Bibliographic Information
Book Title: Approximation Theory
Book Subtitle: Moduli of Continuity and Global Smoothness Preservation
Authors: George A. Anastassiou, Sorin G. Gal
DOI: https://doi.org/10.1007/978-1-4612-1360-4
Publisher: Birkhäuser Boston, MA
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2000
Hardcover ISBN: 978-0-8176-4151-1Published: 22 December 1999
Softcover ISBN: 978-1-4612-7112-3Published: 08 October 2012
eBook ISBN: 978-1-4612-1360-4Published: 06 December 2012
Edition Number: 1
Number of Pages: XIII, 525
Topics: Applications of Mathematics, Approximations and Expansions, Global Analysis and Analysis on Manifolds, Analysis, Computational Mathematics and Numerical Analysis