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＜電子ブック＞
Multivariate Polynomial Approximation / by Manfred Reimer
(International Series of Numerical Mathematics. ISSN:22966072 ; 144)

版	1st ed. 2003.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2003
本文言語	英語
大きさ	X, 358 p : online resource
著者標目	*Reimer, Manfred author SpringerLink (Online service)
件　名	LCSH:Approximation theory LCSH:Numerical analysis FREE:Approximations and Expansions FREE:Numerical Analysis
一般注記	1 Basic Principles and Facts -- 2 Gegenbauer Polynomials -- 3 Multivariate Polynomials -- 4 Polynomials on Sphere and Ball -- 5 Approximation Methods -- 6 Approximation on the Sphere -- 7 Approximation on the Ball -- 8 Tomography -- A Legendre Basis -- B Zeros of the Kernel Function -- C Newman—Shapiro Operators -- D Reconstruction -- E Solutions Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed HTTP:URL=https://doi.org/10.1007/978-3-0348-8095-4

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