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Titlebook: Hyperbolic Cross Approximation; Dinh D?ng,Vladimir Temlyakov,Tino Ullrich,Sergey T Textbook 2018 Springer Nature Switzerland AG 2018 hyper

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發(fā)表于 2025-3-21 17:28:17 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Hyperbolic Cross Approximation
編輯Dinh D?ng,Vladimir Temlyakov,Tino Ullrich,Sergey T
視頻videohttp://file.papertrans.cn/431/430588/430588.mp4
概述Covers both classical results from the 1960s and very recent results on high-dimensional approximation.Contains a number of short illustrative proofs.Provides the first comprehensive survey on hyperbo
叢書名稱Advanced Courses in Mathematics - CRM Barcelona
圖書封面Titlebook: Hyperbolic Cross Approximation;  Dinh D?ng,Vladimir Temlyakov,Tino Ullrich,Sergey T Textbook 2018 Springer Nature Switzerland AG 2018 hyper
描述.This book provides a systematic survey of classical and recent results on hyperbolic cross approximation.. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research..
出版日期Textbook 2018
關(guān)鍵詞hyperbolic cross; sparse grid; mixed smoothness; trigonometric polynomial; linear approximation; Kolmogor
版次1
doihttps://doi.org/10.1007/978-3-319-92240-9
isbn_softcover978-3-319-92239-3
isbn_ebook978-3-319-92240-9Series ISSN 2297-0304 Series E-ISSN 2297-0312
issn_series 2297-0304
copyrightSpringer Nature Switzerland AG 2018
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 20:50:33 | 只看該作者
Function Spaces on ,We begin with the univariate case in order to illustrate the action of the differential operator on periodic functions. For a trigonometric polynomial . we have
板凳
發(fā)表于 2025-3-22 03:08:59 | 只看該作者
Linear Approximation,By linear approximation we understand approximation from a fixed finite-dimensional subspace. In the study of approximation of the univariate periodic functions the idea of representing a function by its Fourier series is very natural and traditional.
地板
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Entropy Numbers,The concept of entropy is also known as Kolmogorov entropy and metric entropy. This concept allows us to measure how big is a compact set.
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Numerical Integration,A cubature rule Λm(f, ξ) approximates the integral I(f) =f. f(x) dx by computing a weighted sum of finitely many function values at X. = {x., . . . , x.},
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發(fā)表于 2025-3-22 23:18:44 | 只看該作者
Related Problems,In this section we briefly discuss the development of the hyperbolic cross approximation theory with emphasis put on the development of methods and connections to other areas of research.
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