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＜電子ブック＞
Hyperbolic Cross Approximation / by Dinh Dũng, Vladimir Temlyakov, Tino Ullrich ; edited by Sergey Tikhonov
(Advanced Courses in Mathematics - CRM Barcelona. ISSN:22970312)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2018
大きさ	XI, 218 p. 24 illus., 11 illus. in color : online resource
著者標目	*Dũng, Dinh author Temlyakov, Vladimir author Ullrich, Tino author Tikhonov, Sergey editor SpringerLink (Online service)
件　名	LCSH:Approximation theory LCSH:Numerical analysis FREE:Approximations and Expansions FREE:Numerical Analysis
一般注記	Introduction -- Trigonometric polynomials -- Function spaces on T^d -- Linear approximation -- Sampling recovery -- Entropy numbers -- Best m-term approximation -- Numerical integration -- Related problems -- High-dimensional approximation -- Appendix 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 HTTP:URL=https://doi.org/10.1007/978-3-319-92240-9

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