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Titlebook: Mathematics of Approximation; Johan Villiers Textbook 2012 Atlantis Press 2012 Best approximation.Fourier series.Polynomial approximation.

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发表于 2025-3-21 18:25:54 | 显示全部楼层 |阅读模式
书目名称Mathematics of Approximation
编辑Johan Villiers
视频video
概述Prerequisites of only calculus and linear algebra.Self-contained and rigorous treatment of the mathematics of approximation.Includes new results,in particular those on local spline interpolation, and
丛书名称Mathematics Textbooks for Science and Engineering
图书封面Titlebook: Mathematics of Approximation;  Johan Villiers Textbook 2012 Atlantis Press 2012 Best approximation.Fourier series.Polynomial approximation.
描述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 topicsinclude 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
出版日期Textbook 2012
关键词Best approximation; Fourier series; Polynomial approximation; Quadrature; Spline approximation
版次1
doihttps://doi.org/10.2991/978-94-91216-50-3
isbn_softcover978-94-6239-046-1
isbn_ebook978-94-91216-50-3Series ISSN 2213-0853 Series E-ISSN 2213-087X
issn_series 2213-0853
copyrightAtlantis Press 2012
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发表于 2025-3-21 23:09:54 | 显示全部楼层
Johan de Villiersphysically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers con978-3-528-08098-3978-3-322-87869-4Series ISSN 1612-2909 Series E-ISSN 1860-0824
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Polynomial Interpolation Formulas,e sample set of distinct points inthe domain of f , if P is obtained to satisfy the condition that P agrees with f on the sampleset. The objective of this chapter is to establish a fundamental existence and uniquenessresult for polynomial interpolation as well as to derive explicit formulations of t
发表于 2025-3-22 08:59:06 | 显示全部楼层
Polynomial Uniform Convergence,rors converges uniformly to zero on .. In this chapter, we first show that such convergence is not guaranteed in the case that the polynomials are constructed to interpolate . on some sequence of equally-spaced sample point sets with cardinalities increasing to infinity.
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Spline Approximation,esirable approximation accuracy by increasing the polynomial degrees, at the expense of increasing computational complexity and undesirable features, such as increase in oscillation of the polynomial approximant. To avoid the increase of polynomial degrees, this chapter is devoted to the study of ap
发表于 2025-3-22 22:46:55 | 显示全部楼层
Johan de Villiers two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the w
发表于 2025-3-23 04:23:16 | 显示全部楼层
Spline Approximation,such as increase in oscillation of the polynomial approximant. To avoid the increase of polynomial degrees, this chapter is devoted to the study of approximation by piecewise polynomials with fixed degrees, while achieving arbitrarily desirable approximation accuracy by allowing the decrease in spacing of the break-points of the polynomial pieces.
发表于 2025-3-23 07:16:57 | 显示全部楼层
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