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＜電子ブック＞
Mathematics of Approximation / by Johan De Villiers
(Mathematics Textbooks for Science and Engineering. ISSN:2213087X ; 1)

版	1st ed. 2012.
出版者	(Paris : Atlantis Press : Imprint: Atlantis Press)
出版年	2012
本文言語	英語
大きさ	XXI, 406 p : online resource
著者標目	*De Villiers, Johan author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Approximation theory LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Mathematics FREE:Computational Mathematics and Numerical Analysis FREE:Approximations and Expansions FREE:Mathematics of Computing FREE:Mathematical and Computational Engineering Applications
一般注記	Polynomial Interpolation Formulas -- Error Analysis For Polynomial Interpolation -- Polynomial Uniform Convergence -- Best Approximation -- Approximation Operators -- Best Uniform Polynomial Approximation -- Orthogonality -- Interpolatory Quadrature -- Approximation of Periodic Functions -- Spline Approximation The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter HTTP:URL=https://doi.org/10.2991/978-94-91216-50-3

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