Shape-Preserving Approximation by Real and Complex Polynomials

Gal, Sorin G.

ISBN 10: 0817647023 / ISBN 13: 9780817647025

Edité par Birkhauser Boston Inc, 2008

This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems that arise in science and engineering and require an optimal mathematical representation of physical reality. Num Pages: 365 pages, biography. BIC Classification: PBF. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 156 x 20. Weight in Grams: 691. . 2008. Hardback. . . . . Books ship from the US and Ireland. N° de réf. du vendeur V9780817647025

Synopsis :

In many problems arising in engineering and science one requires approxi- tion methods to reproduce physical reality as well as possible. Very schema- cally, if the input data represents a complicated discrete/continuous quantity of information, of "shape" S (S could mean, for example, that we have a "monotone/convex" collection of data), then one desires to represent it by the less-complicated output information, that "approximates well" the input data and, in addition, has the same "shape" S. This kind of approximation is called "shape-preserving approximation" and arises in computer-aided geometric design, robotics, chemistry, etc. Typically, the input data is represented by a real or complex function (of one or several variables), and the output data is chosen to be in one of the classes polynomial, spline, or rational functions. The present monograph deals in Chapters 1-4 with shape-preserving - proximation by real or complex polynomials in one or several variables. Chapter 5 is an exception and is devoted to some related important but n- polynomial andnonsplineapproximations preservingshape.Thesplinecaseis completely excluded in the present book, since on the one hand, many details concerning shape-preserving properties of splines can be found, for example, in the books of de Boor [49], Schumaker [344], Chui [69], DeVore-Lorentz [91], Kvasov [218] and in the surveys of Leviatan [229], Koci´ c-Milovanovi´ c [196], while on the other hand, we consider that shape-preserving approximation by splines deserves a complete study in a separate book.

Détails bibliographiques

Titre : Shape-Preserving Approximation by Real and ...
Éditeur : Birkhauser Boston Inc
Date d'édition : 2008
Reliure : Couverture rigide
Etat : New