Approximation Theory Using Positive Linear Operators

Radu Paltanea

210 pages, parution le 31/10/2004

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Résumé

This work treats quantitative aspects of the approximation of functions using positive linear operators. The theory of these operators has been an important area of research in the last few decades, particularly as it affects computer-aided geometric design. In this book, the crucial role of the second order moduli of continuity in the study of such operators is emphasized. New and efficient methods, applicable to general operators and to diverse concrete moduli, are presented. The advantages of these methods consist in obtaining improved and even optimal estimates, as well as in broadening the applicability of the results.

Additional Topics and Features:

Examination of the multivariate approximation case
Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators
Many general estimates, leaving room for future applications (e.g. the B-spline case)
Extensions to approximation operators acting on spaces of vector functions
Historical perspective in the form of previous significant results

This monograph will be of interest to those working in the field of approximation or functional analysis. Requiring only familiarity with the basics of approximation theory, the book may serve as a good supplementary text for courses in approximation theory, or as a reference text on the subject.

Written for:
Graduate students, postdocs and higher qualified scientists in mathematics and computer science interested in the fields of Geometric Modeling, Computer Aided Geometric Design, Image Processing, Real Analysis and Approximation Theory

Sommaire

Introduction
Estimates with second order moduli
Absolute optimal constants
Estimates for the Bernstein operators
Two classes of Bernstein type operators
Approximation operators for vector valued function
References

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Radu Paltanea
Parution	31/10/2004
Nb. de pages	210
Format	15 x 23,5
Couverture	Broché
Poids	370g
Intérieur	Noir et Blanc
EAN13	9780817643508
ISBN13	978-0-8176-4350-8