Multivariate Approximation
Published on 27. June 2018
978-1-108-60863-3 (ISBN)
Description
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.
Reviews / Votes
'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, MathSciNetMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 12 Line drawings, black and white
File size
5,34 MB
ISBN-13
978-1-108-60863-3 (9781108608633)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
V. Temlyakov
Multivariate Approximation
Book
07/2018
Cambridge University Press
€139.80
Shipment within 15-20 days
Person
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.
Content
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.
