Approximation Theory Using Positive Linear Operators
Contributors: George A. Anastassiou (Adapter)
Edition: 1 edition
Publisher: Birkhäuser Boston
Published: September 17, 2004
Language: eng
Format: Paperback
Number of pages: 202
ISBN-13: 9780817643508
Subjects: Functional analysis; Mathematical foundations; Mathematical Analysis; Approximation theory; Mathematics; Science/Mathematics; Algebra - General; Applied; Mathematics / Mathematical Analysis; General; Linear operators
First sentence: The most constructive proofs of the Weierstrass theorem concerning the approximation of continuous functions on a compact interval by polynomials use some sequences of linear positive operators.
Description: 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.