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Hyperbolic cross approximation

Dung, Dinh.

Hyperbolic cross approximation

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hyperbolic cross approximationby Dinh Dung, Vladimir Temlyakov, Tino Ullrich ; edited by Sergey Tikhonov.
Author:	Dung, Dinh.
other author:	Temlyakov, Vladimir.
Published:	Cham :Springer International Publishing :2018.
Description:	xi, 218 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Approximation theory.
Online resource:	https://doi.org/10.1007/978-3-319-92240-9
ISBN:	9783319922409$q(electronic bk.)

Hyperbolic cross approximation
Dung, Dinh.

Hyperbolic cross approximation[electronic resource] /by Dinh Dung, Vladimir Temlyakov, Tino Ullrich ; edited by Sergey Tikhonov. - Cham :Springer International Publishing :2018. - xi, 218 p. :ill. (some col.), digital ;24 cm. - Advanced courses in mathematics - CRM Barcelona,2297-0304. - Advanced courses in mathematics - CRM Barcelona..

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.

ISBN: 9783319922409$q(electronic bk.)

Standard No.: 10.1007/978-3-319-92240-9doiSubjects--Topical Terms:

185327
Approximation theory.

LC Class. No.: QA221 / .D755 2018

Dewey Class. No.: 511.4

Hyperbolic cross approximation
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245 1 0 $a Hyperbolic cross approximation $h [electronic resource] / $c by Dinh Dung, Vladimir Temlyakov, Tino Ullrich ; edited by Sergey Tikhonov.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2018.
300 $a xi, 218 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Advanced courses in mathematics - CRM Barcelona, $x 2297-0304
505 0 $a 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.
520 $a 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.
650 0 $a Approximation theory. $3 185327
650 0 $a Differential equations, Hyperbolic. $3 199039
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650 1 4 $a Approximations and Expansions. $3 281039
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700 1 $a Temlyakov, Vladimir. $3 715975
700 1 $a Ullrich, Tino. $3 824912
700 1 $a Tikhonov, Sergey. $3 684038
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950 $a Mathematics and Statistics (Springer-11649)