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Author Gal, Sorin G
Title Shape-Preserving Approximation by Real and Complex Polynomials
Imprint Boston, MA : Springer Basel AG, 2008
©2008
book jacket
Descript 1 online resource (364 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- CONTENTS -- Preface -- 1 Shape-Preserving Approximation by Real Univariate Polynomials -- 1.1 Introduction -- 1.2 Shape-Preserving Interpolation by Polynomials -- 1.3 Bernstein-Type Polynomials Preserving Shapes -- 1.4 Shisha-Type Results -- 1.5 Positive and Copositive Polynomial Approximation -- 1.6 Monotone and Comonotone Polynomial Approximation -- 1.7 Convex and Coconvex Polynomial Approximation -- 1.8 Shape-Preserving Approximation by Convolution Polynomials -- 1.9 Positive Linear Polynomial Operators Preserving Shape -- 1.10 Notes -- 2 Shape-Preserving Approximation by Real Multivariate Polynomials -- 2.1 Introduction -- 2.2 Bernstein-Type Polynomials Preserving Shapes -- 2.3 Shisha-Type Methods and Generalizations -- 2.4 Approximation Preserving Three Classical Shapes -- 2.5 Bivariate Monotone Approximation by Convolution Polynomials -- 2.6 Tensor Product Polynomials Preserving Popoviciu's Convexities -- 2.7 Bibliographical Notes and Open Problems -- 3 Shape-Preserving Approximation by Complex Univariate Polynomials -- 3.1 Introduction -- 3.2 Shisha-Type Methods and Generalizations -- 3.3 Shape-Preserving Approximation by Convolution Polynomials -- 3.4 Approximation and Geometric Properties of Bernstein Polynomials -- 3.5 Bibliographical Notes and Open Problems -- 4 Shape-Preserving Approximation by Complex Multivariate Polynomials -- 4.1 Introduction -- 4.2 Bernstein-Type Polynomials Preserving Univalence -- 4.3 Shape-Preserving Approximation by Other Types of Polynomials -- 4.4 Bibliographical Notes and Open Problems -- 5 Appendix: Some Related Topics -- 5.1 Shape-Preserving Approximation by General Linear Operators on C[a, b] -- 5.2 Some Real and Complex Nonpolynomial Operators Preserving Shape -- 5.3 Shape-Preserving Polynomial Approximation in Ordered Vector Spaces -- 5.4 Complex Nonpolynomial Convolutions Preserving Shape
5.5 Bibliographical Notes and Open Problems -- References -- Index
First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variablesOf interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineeringContains many open problems to spur future researchRich and updated bibliography
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Gal, Sorin G. Shape-Preserving Approximation by Real and Complex Polynomials Boston, MA : Springer Basel AG,c2008 9780817647025
Subject Bernstein polynomials
Electronic books
Alt Author Anastassiou, George A
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