| 書目名稱 | Lectures on Constructive Approximation | | 副標(biāo)題 | Fourier, Spline, and | | 編輯 | Volker Michel | | 視頻video | http://file.papertrans.cn/584/583490/583490.mp4 | | 概述 | Combines an explanation of classical and modern approximation methods for Euclidean and spherical geometries.Detailed explanations and illustrations included to optimize the understanding of topics.Co | | 叢書名稱 | Applied and Numerical Harmonic Analysis | | 圖書封面 |  | | 描述 | .Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball .focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets..Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include:.* the advantages and disadvantages of Fourier, spline, and wavelet methods.* theory and numerics of orthogonal polynomials on intervals, spheres, and balls.* cubic splines and splines based on reproducing kernels.* multiresolution analysis using wavelets and scaling functions.This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. | | 出版日期 | Textbook 2013 | | 關(guān)鍵詞 | Fourier transform; Fourier transform; Fourier transform; orthogonal polynomials; orthogonal polynomials; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-8403-7 | | isbn_ebook | 978-0-8176-8403-7Series ISSN 2296-5009 Series E-ISSN 2296-5017 | | issn_series | 2296-5009 | | copyright | Springer Science+Business Media New York 2013 |
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