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. New and efficient methods, applicable to Bernstein operators and to diverse concrete moduli, are presented in this book. The advantages of these methods consist in obtaining improved and even optimal estimates, as well as in broadening the applicability of the 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.
Rezensionen / Stimmen
From the reviews:
"This monograph will be of interest to those working in the field of approximation, and it may serve as a good supplementary text for courses in approximation theory, or as a reference text on the subject."(ZENTRALBLATT MATH)
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 12 mm
Gewicht
ISBN-13
978-0-8176-4350-8 (9780817643508)
DOI
10.1007/978-1-4612-2058-9
Schweitzer Klassifikation
1 Introduction.- 1.1 Operators and functionals. Moduli of continuity.- 1.2 Approximation of functions by sequences of positive linear operators.- 2 Estimates with Second Order Moduli.- 2.1 A general approach.- 2.2 Estimates with moduli ?2? and ?2?.- 2.3 Estimates with modulus ?2d.- 2.4 Estimates with modulus ?2dd.- 2.5 Estimates with Ditzian-Totik modulus.- 3 Absolute Optimal Constants.- 3.1 Introduction.- 3.2 Discrete functionals and the classical second order modulus ?2.- 3.3 General functionals and the second order modulus with parameter ?2?.- 4 Estimates for the Bernstein Operators.- 4.1 Various types of estimates.- 4.2 Best constant in the estimate with modulus ?2.- 4.3 Global smoothness preservation.- 5 Two Classes of Bernstein Type Operators.- 5.1 Generalized Brass type operators.- 5.2 Generalized Durrmeyer type operators.- 6 Approximation Operators for Vector-Valued Functions.- 6.1 Approximation of functions with real argument.- 6.2 Approximation of functions with vector argument.- References.
