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.
Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.
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.
'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
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