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Noisy Information and Computational Complexity

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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 worst case, average case, mixed worst-average, average-worst, and asymptotic. Particular topics 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.

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Noisy Information and Computational Complexity, Leszek Plaskota

Sprache
Erscheinungsdatum
1996
Einband
(Hardcover),
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Beschädigt
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42,99 €inkl. MwSt.

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Titel
Noisy Information and Computational Complexity
Sprache
Englisch
Autor*innen
Leszek Plaskota
Erscheinungsdatum
1996
Einband
Hardcover
Seitenzahl
324
ISBN10
0521553687
ISBN13
9780521553681
Reihe
Beschreibung
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 worst case, average case, mixed worst-average, average-worst, and asymptotic. Particular topics 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.