Approximation Of Set-Valued Functions: Adaptation Of Classical Approximation Operators, Dyn Nira Et Al

Автор: Bede
Название: Approximation by Max-Product Type Operators
ISBN: 331934188X ISBN-13(EAN): 9783319341880
Издательство: Springer
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Описание: This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called 'max-product' type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several.Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility.Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.

Автор: G?rtner, Matousek
Название: Approximation Algorithms and Semidefinite Programming
ISBN: 3642220142 ISBN-13(EAN): 9783642220142
Издательство: Springer
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Цена: 9781.00 р.
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Описание: Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material.  There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms. This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.

Автор: Breuillard
Название: Thin Groups and Superstrong Approximation
ISBN: 1107036852 ISBN-13(EAN): 9781107036857
Издательство: Cambridge Academ
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Описание: This collection of survey and research articles focuses on recent developments in quantitative aspects of `thin groups`. It provides a broad panorama of a very active field at the boundary between geometry, dynamical systems, number theory and combinatorics for professional mathematicians and graduate students in this fascinating area of research.