Overview
- 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 hyperbolic cross approximation of the mixed smoothness classes of multivariate functions
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (11 chapters)
Keywords
- hyperbolic cross
- sparse grid
- mixed smoothness
- trigonometric polynomial
- linear approximation
- Kolmogorov width
- linear width
- orthowidth
- sampling recovery
- sampling width
- nonlinear approximation
- entropy number
- best m-term approximation
- numerical integration
- cubature formulas
- high-dimensional approximation
About this book
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.
Authors, Editors and Affiliations
About the editor
Dinh Dũng is a Professor at the Vietnam National University, Vietnam.
Vladimir Temlyakov is a Professor at the University of South Carolina, CA, USA.
Tino Ullrich is a Professor at the Institute for Numerical Simulation in Bonn, Germany.
Bibliographic Information
Book Title: Hyperbolic Cross Approximation
Authors: Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
Editors: Sergey Tikhonov
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-319-92240-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-92239-3Published: 13 November 2018
eBook ISBN: 978-3-319-92240-9Published: 02 November 2018
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: XI, 218
Number of Illustrations: 13 b/w illustrations, 11 illustrations in colour