Greedy Approximation

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Cambridge University Press, Sep 8, 2011 - Computers
This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.
 

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Contents

1 Greedy approximation with regard to bases
1
Hilbert spaces
77
3 Entropy
143
4 Approximation in learning theory
183
5 Approximation in compressed sensing
277
Banach spaces
334
References
405
Index
415
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About the author (2011)

Vladimir Temlyakov is Carolina Distinguished Professor in the Department of Mathematics at the University of South Carolina.

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