The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
Greedy Approximation
Abstract
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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Citations
Cites
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Matching pursuits with time-frequency dictionaries
Mallat, S. G., & Zhang, Z. (1993) · IEEE Transactions on Signal Processing · doi:10.1109/78.258082 · Cited by 9,112
Ideal spatial adaptation by wavelet shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.1093/biomet/81.3.425 · Cited by 8,760
Decoding by Linear Programming
Candes, E. J., & Tao, T. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.858979 · Cited by 7,121
Stable signal recovery from incomplete and inaccurate measurements
Candès, E. J., Romberg, J. K., & Tao, T. (2006) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20124 · Cited by 7,036
Atomic Decomposition by Basis Pursuit
Chen, S. S., Donoho, D. L., & Saunders, M. A. (2001) · SIAM Review · doi:10.1137/s003614450037906x · Cited by 5,085
Greed is Good: Algorithmic Results for Sparse Approximation
Tropp, J. A. (2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.834793 · Cited by 3,635
Entropy-based algorithms for best basis selection
Coifman, R. R., & Wickerhauser, M. V. (1992) · IEEE Transactions on Information Theory · doi:10.1109/18.119732 · Cited by 3,188
Universal approximation bounds for superpositions of a sigmoidal function
Barron, A. R. (1993) · IEEE Transactions on Information Theory · doi:10.1109/18.256500 · Cited by 2,804
DeVore, R. A., & Lorentz, G. G. (1993) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-662-02888-9 · Cited by 2,352
Metadata
- Authors
- Temlyakov, V.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2011-09-08
- Volume
- 17
- Pages
- 235-409
- OpenAlex
- W2913975905
- Cited by
- 409
- References
- 36
- FWCI
- 1.97
- Type
- book
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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