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 |  | 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 | doi | https://doi.org/10.2991/978-94-91216-50-3 | isbn_softcover | 978-94-6239-046-1 | isbn_ebook | 978-94-91216-50-3Series ISSN 2213-0853 Series E-ISSN 2213-087X | issn_series | 2213-0853 | copyright | Atlantis Press 2012 |
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