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Greedy Approximation

$89.99 (P)

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: October 2011
  • availability: Available
  • format: Hardback
  • isbn: 9781107003378

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About the Authors
  • 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.

    • The first book on the hot topic of greedy approximation
    • Developed from the author's first-class review published in Acta Numerica
    • Covers classical results as well as the latest advances, and material has been tried and tested by the author in several graduate courses
    • Open problems provide inspiration for further research
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    Reviews & endorsements

    "The book is written in a mathematically rigorous but clear and readable style. It is completely self-contained; Temlyakov includes all of the necessary background information. Therefore, it is certainly a well-suited textbook for graduate courses. Moreover, graduate students and professional researchers who are prepared to work their way through the classical mathematical definition-theorem-proof style should read the book on their own--they will greatly benefit from its excellent introduction to a highly interesting and novel area of applied mathematics."
    Kai Diethelm, Computing Reviews

    "The author is the leading expert on greedy approximation and this book offers a guided tour through the state of the art of the subject. Temlyakov's book is an excellent mathematical monograph and a valuable reference for researchers not only in approximation theory, but also in numerical mathematics, analysis, functional analysis, and statistics. The book is addressed mainly to researchers interested in greedy approximation and related areas. However, it is written at a level that is approachable for graduate students interested in the aforementioned areas, and it could be used for designing graduate courses in greedy approximation, learning theory and compressed sensing. As an added bonus, the author has included an extensive list of open problems in the area that can serve as inspiration for future research papers and dissertations."
    Morten Nielsen, SIAM News

    "This is an excellent book on theory of greedy approximation, a part of non linear approximation. To the best of my knowledge, it is the first book completely devoted to this subject."
    Marcello Sanguineti, Mathematical Reviews

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    Product details

    • Date Published: October 2011
    • format: Hardback
    • isbn: 9781107003378
    • length: 432 pages
    • dimensions: 235 x 156 x 25 mm
    • weight: 0.76kg
    • availability: Available
  • Table of Contents

    Preface
    1. Greedy approximation with respect to bases
    2. Greedy approximation with respect to dictionaries: Hilbert spaces
    3. The entropy
    4. Approximation in learning theory
    5. Approximation in compressed sensing
    6. Greedy approximation with respect to dictionaries: Banach spaces
    References
    Index.

  • Author

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

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