Multivariate Approximation

V. Temlyakov (University of South Carolina)

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English

Cambridge University Press
19 July 2018

Numerical analysis; Computer vision; Signal processing; Image processing

Series: Cambridge Monographs on Applied and Computational Mathematics

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.

By: V. Temlyakov (University of South Carolina)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 32
Dimensions: Height: 253mm, Width: 178mm, Spine: 34mm
Weight: 1.120kg
ISBN: 9781108428750
ISBN 10: 1108428754
Series: Cambridge Monographs on Applied and Computational Mathematics
Pages: 550
Publication Date: 19 July 2018
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

V. Temlyakov is Carolina Distinguished Professor in the Department of Mathematics at the University of South Carolina. He has written several books on approximation theory, and has received numerous honours and awards. His research interests include greedy approximation, compressed sensing, learning theory and numerical integration.

Reviews for Multivariate Approximation

'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 first 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