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Hyperbolic Cross Approximation / by Dinh Dũng, Vladimir Temlyakov, Tino Ullrich ; edited by Sergey Tikhonov.
Springer Nature - Springer Mathematics and Statistics eBooks 2018 English International Available online
View online- Format:
- Book
- Author/Creator:
- Dũng, Dinh, author.
- Temli︠a︡kov, V. N. (Vladimir Nikolaevich), author.
- Ullrich, Tino, 1980- author.
- Series:
- Mathematics and Statistics (Springer-11649)
- Advanced courses in mathematics, CRM Barcelona 2297-0304
- Advanced Courses in Mathematics - CRM Barcelona, 2297-0304
- Language:
- English
- Subjects (All):
- Approximation theory.
- Numerical analysis.
- Approximations and Expansions.
- Numerical Analysis.
- Local Subjects:
- Approximations and Expansions.
- Numerical Analysis.
- Physical Description:
- 1 online resource (XI, 218 pages) : 24 illustrations, 11 illustrations in color.
- Edition:
- First edition 2018.
- Contained In:
- Springer eBooks
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
- System Details:
- text file PDF
- Summary:
- 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.
- Contents:
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-319-92240-9
- 9783319922409
- Access Restriction:
- Restricted for use by site license.
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