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Multivariate Approximation V. Temlyakov (University of South Carolina)

Multivariate Approximation By V. Temlyakov (University of South Carolina)

Summary

Starting from classical linear approximation, this is a self-contained presentation of modern multivariate approximation theory that explores its connections with other areas of mathematics. The prerequisites are no more than standard undergraduate mathematics, so the book will be accessible to graduate students and non-specialists.

Multivariate Approximation Summary

Multivariate Approximation by V. Temlyakov (University of South Carolina)

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.

Multivariate Approximation Reviews

'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

About V. Temlyakov (University of South Carolina)

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.

Table of Contents

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.

Additional information

NPB9781108428750
9781108428750
1108428754
Multivariate Approximation by V. Temlyakov (University of South Carolina)
New
Hardback
Cambridge University Press
2018-07-19
550
N/A
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