Handbook of Approximation Algorithms and Metaheuristics, 

Автор: Trefethen
Название: Approximation Theory and Approximation Practice
ISBN: 1611972396 ISBN-13(EAN): 9781611972399
Издательство: Mare Nostrum (Eurospan)
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Цена: 55440.00 T
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Описание: In a book that will appeal to beginners and experts alike, Oxford University’s Nick Trefethen presents approximation theory using a fresh approach for this established field.Approximation Theory and Approximation Practice is a textbook on classical polynomial and rational approximation theory for the twenty-first century. It uses MATLAB? to teach the field’s most important ideas and results and differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable Matlab M-file, available online.In addition, the book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment.Each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation.

Автор: Willy Do?rfler
Название: Photonic Crystals : Mathematical Analysis And Numerical Approximation
ISBN: 3034801122 ISBN-13(EAN): 9783034801126
Издательство: Springer
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Цена: 27940.00 T
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Описание: <p>This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers.</p><p>In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of continuous and discrete spectrum, multiple scales in space and time, and the ill-posedness of these problems.</p><p>This volume collects a series of lectures which introduce into the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.</p>

Автор: G?rtner, Matousek
Название: Approximation Algorithms and Semidefinite Programming
ISBN: 3642220142 ISBN-13(EAN): 9783642220142
Издательство: Springer
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Цена: 65210.00 T
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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: Christos Kaklamanis; Martin Skutella
Название: Approximation and Online Algorithms
ISBN: 3540779175 ISBN-13(EAN): 9783540779179
Издательство: Springer
Цена: 65210.00 T
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Автор: Ashish Goel; Klaus Jansen; Jos? Rolim; Ronitt Rubi
Название: Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques
ISBN: 3540853626 ISBN-13(EAN): 9783540853626
Издательство: Springer
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Цена: 97820.00 T
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Описание: Constitutes the joint refereed proceedings of the 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and the 12th International Workshop on Randomization and Computation, RANDOM 2008, held in Boston, MA, USA, in August 2008. This book reviews 20 revised papers of the APPROX 2008 workshop.

Автор: Komornik, Vilmos
Название: Topology, calculus and approximation
ISBN: 1447173155 ISBN-13(EAN): 9781447173151
Издательство: Springer
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Цена: 32600.00 T
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Описание: Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejer, Stieltjes, and Turan.

The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Caratheodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations.
Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple yet pertinent examples and exercises illustrate the usefulness of most theorems. Many of these examples are new or difficult to locate in the literature, and so the original sources of most notions and results are given to help readers understand the development of the field.