Автор: Bede Название: Approximation by Max-Product Type Operators ISBN: 331934188X ISBN-13(EAN): 9783319341880 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
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: Emmanuil H Georgoulis; Armin Iske; Jeremy Levesley Название: Approximation Algorithms for Complex Systems ISBN: 3642266657 ISBN-13(EAN): 9783642266652 Издательство: Springer Рейтинг: Цена: 29209.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Part I INVITED SURVEYS: Emergent Behaviour in Large Electrical Networks by D. P. Almond, C.J. Budd, N.J. McCullen.- Algorithms and Error Bounds for Multivariate Piecewise Constant Approximation by O. Davydov.- Anisotropic Triangulation Methods in Adaptive Image Approximation by L. Demaret, A. Iske.- Form Assessment in Coordinate Metrology by A.B. Forbes and H.D.Minh.- Discontinuous Galerkin Methods for Linear Problems: An Introduction by E. H. Georgoulis.- A Numerical Analyst's View of the Lattice Boltzmann Method by A. G. Gorban, J. Levesley, D. Packwood.- Approximating Probability Measures on Manifolds via Radial Basis Functions by J. Levesley, X. Sun.- Part II CONTRIBUTED RESEARCH PAPERS: Modelling Clinical Decay Data Using Exponential Functions by M.G. Cox.- Towards Calculating the Basin of Attraction of Non-Smooth Dynamical Systems Using Radial Basis Functions by P. Giesl.- Stabilizing Lattice Boltzmann Simulation of Fluid Flow past a Circular Cylinder with Ehrenfests' Limiter by T.S. Khan, J. Levesley.- Fast and Stable Interpolation of Well Data Using the Norm Function by B. Li, J. Levesley.- Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data by I. Markovsky.- On Bivariate Interpolatory Mask Symbols, Subdivision and Refinable Functions by A. F. Rabarison, J. de Villiers.- Model and Feature Selection in Metrology Data Approximation by X. Yang, A. B. Forbes.
Автор: Evripidis Bampis; Martin Skutella Название: Approximation and Online Algorithms ISBN: 3540939792 ISBN-13(EAN): 9783540939795 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Constitutes the refereed post workshop proceedings of the 6th International Workshop on Approximation and Online Algorithms, WAOA 2008, held in Karlsruhe, Germany, in September 2008 as part of the ALGO 2008 conference event. This title includes 22 revised full papers that were reviewed and selected from 56 submissions.
Описание: Contains 41 reviewed papers, selected by the two program committees from a total of 101 submissions. Among the issues addressed are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, and more.
Описание: This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.
Описание: Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
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