Description: Multivariate Approximation Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation. V. Temlyakov (Author) 9781108428750, Cambridge University Press Hardback, published 19 July 2018 550 pages 25.3 x 17.8 x 3.4 cm, 1.12 kg 'This excellent book covers a variety of topics in univariate and multivariate approximation as well as their connection to computational mathematics … The exposition is designed in such a way that the reader is familiarized with the univariate results ?rst and then the transition to the multivariate case is performed, highlighting the challenges and the new methods. The book is self-contained and is accessible to readers with graduate and advanced undergraduate background.' Andriy V. Prymak, MathSciNet This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area. 1. Approximation of univariate functions 2. Optimality and other properties of the trigonometric system 3. Approximation of functions from anisotropic Sobolev and Nikol'skii classes 4. Hyperbolic cross approximation 5. The widths of classes of functions with mixed smoothness 6. Numerical integration and approximate recovery 7. Entropy 8. Greedy approximation 9. Sparse approximation Appendix. Classical inequalities References Index. Subject Areas: Image processing [UYT], Signal processing [UYS], Computer vision [UYQV], Numerical analysis [PBKS]
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BIC Subject Area 1: Image processing [UYT]
BIC Subject Area 2: Signal processing [UYS]
BIC Subject Area 3: Computer vision [UYQV]
BIC Subject Area 4: Numerical analysis [PBKS]
Number of Pages: 550 Pages
Language: English
Publication Name: Multivariate Approximation
Publisher: Cambridge University Press
Publication Year: 2018
Subject: Computer Science, Mathematics
Item Height: 253 mm
Item Weight: 1120 g
Type: Textbook
Author: V. Temlyakov
Series: Cambridge Monographs on Applied and Computational Mathematics
Item Width: 178 mm
Format: Hardcover
