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Noisy Information and Computational Complexity

CAD$65.95 (C)

  • Date Published: March 2012
  • availability: Available
  • format: Paperback
  • isbn: 9780521349444

CAD$ 65.95 (C)

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About the Authors
  • This book deals with the computational complexity of mathematical problems for which available information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; he considers deterministic as well as stochastic noise. He also presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average, average-worst, and asymptotic. Particular topics include: the existence of optimal linear (affine) algorithms, optimality properties of smoothing spline, regularization and least squares algorithms (with the optimal choice of the smoothing and regularization parameters), adaption versus nonadaption, and relations between different settings. The book integrates the work of researchers over the past decade in such areas as computational complexity, approximation theory, and statistics, and includes many new results as well. The author supplies two hundred exercises to increase the reader's understanding of the subject.

    • Was the first book where noisy information is studied in the context of computational complexity
    • Integrates results of researchers from several fields: computational complexity, approximation theory and statistics
    • Can be used as an advanced textbook
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    Reviews & endorsements

    "The monograph is well organized and carefully written. It serves as an excellent reference book for branch of computational complexity. It is relevant also to statisticians and to applied mathematicians who analyze algorithms for problems for problems with noisy data." Klaus Ritter, Mathematical Reviews

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    Product details

    • Date Published: March 2012
    • format: Paperback
    • isbn: 9780521349444
    • length: 322 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.48kg
    • availability: Available
  • Table of Contents

    1. Overview
    2. Worst case setting
    3. Average case setting
    4. Worst-average case setting
    5. Average-worst case setting
    6. Asymptotic setting

  • Author

    Leszek Plaskota, Uniwersytet Warszawski, Poland

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