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Approximation Theory, George A. Anastassiou; Sorin G. Gal


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Автор: George A. Anastassiou; Sorin G. Gal
Название:  Approximation Theory
ISBN: 9781461271123
Издательство: Springer
Классификация:





ISBN-10: 1461271126
Обложка/Формат: Paperback
Страницы: 525
Вес: 0.75 кг.
Дата издания: 08.10.2012
Язык: English
Размер: 234 x 156 x 28
Основная тема: Mathematics
Подзаголовок: Moduli of Continuity and Global Smoothness Preservation
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val- ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop- erty (GSPP) for almost all known linear approximation operators of ap- proximation theory including: trigonometric operators and algebraic in- terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera- tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat- ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth- ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.


Towards Intelligent Modeling: Statistical Approximation Theory

Автор: George A. Anastassiou; Oktay Duman
Название: Towards Intelligent Modeling: Statistical Approximation Theory
ISBN: 364226817X ISBN-13(EAN): 9783642268175
Издательство: Springer
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Цена: 21661.00 р.
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Описание: Statistical convergence has been explored in numerous contexts such as fuzzy logic theory. Here, the authors approach the subject by approximating a function by linear operators, focusing on situations in which the classical limit is not effective.

Approximation Methods in Probability Theory

Автор: ?ekanavi?ius
Название: Approximation Methods in Probability Theory
ISBN: 3319340719 ISBN-13(EAN): 9783319340715
Издательство: Springer
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Цена: 7965.00 р.
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Описание: This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems.While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

Progress in approximation theory and applicable complex analysis

Название: Progress in approximation theory and applicable complex analysis
ISBN: 3319492403 ISBN-13(EAN): 9783319492407
Издательство: Springer
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Цена: 16769.00 р.
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Описание: Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies.

Advances in Applied Mathematics and Approximation Theory

Автор: Anastassiou George A
Название: Advances in Applied Mathematics and Approximation Theory
ISBN: 1461463920 ISBN-13(EAN): 9781461463924
Издательство: Springer
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Цена: 16769.00 р.
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Описание: Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at "Applied Mathematics and Approximation Theory 2012," an international conference held in Ankara, Turkey, May 17-20, 2012.

Fuzzy Mathematics: Approximation Theory

Автор: George A. Anastassiou
Название: Fuzzy Mathematics: Approximation Theory
ISBN: 3642112196 ISBN-13(EAN): 9783642112195
Издательство: Springer
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Цена: 26122.00 р.
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Описание: The theory presented in this book is destined and expected to find applications to all aspects of fuzziness from theoretical to practical in almost all sciences, technology, finance and industry, as well as within pure mathematics.

Frontiers In Approximation Theory

Автор: Anastassiou George A
Название: Frontiers In Approximation Theory
ISBN: 9814696080 ISBN-13(EAN): 9789814696081
Издательство: World Scientific Publishing
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Цена: 13939.00 р.
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Описание:

This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.

The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.

The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.

Mathematical Analysis, Approximation Theory and Their Applications

Автор: Rassias
Название: Mathematical Analysis, Approximation Theory and Their Applications
ISBN: 3319312790 ISBN-13(EAN): 9783319312798
Издательство: Springer
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Цена: 23058.00 р.
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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.

Intelligent Mathematics II: Applied Mathematics and Approximation Theory

Автор: George A. Anastassiou; Oktay Duman
Название: Intelligent Mathematics II: Applied Mathematics and Approximation Theory
ISBN: 3319303201 ISBN-13(EAN): 9783319303208
Издательство: Springer
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Цена: 39182.00 р.
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Описание: This specialvolume is a collection of outstanding more applied articles presented in AMAT2015 held in Ankara, May 28-31, 2015, at TOBB Economics and TechnologyUniversity.The collectionis suitable for Applied and Computational Mathematics and Engineeringpractitioners, also for related graduate students and researchers.

Approximation Theory XV: San Antonio 2016

Автор: Gregory E. Fasshauer; Larry L. Schumaker
Название: Approximation Theory XV: San Antonio 2016
ISBN: 3319599119 ISBN-13(EAN): 9783319599113
Издательство: Springer
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Цена: 22359.00 р.
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Описание:

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22-25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type.

The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.

Approximation Theory XIII: San Antonio 2010

Автор: Marian Neamtu; Larry L. Schumaker
Название: Approximation Theory XIII: San Antonio 2010
ISBN: 1489997105 ISBN-13(EAN): 9781489997104
Издательство: Springer
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Цена: 25853.00 р.
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Описание: These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States. Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.

Methods of fourier analysis and approximation theory

Название: Methods of fourier analysis and approximation theory
ISBN: 3319274651 ISBN-13(EAN): 9783319274652
Издательство: Springer
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Цена: 11878.00 р.
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Описание: Different facets of interplay between harmonic analysis andapproximation theory are covered in this volume. The topics included areFourier analysis, function spaces, optimization theory, partial differentialequations, and their links to modern developments in the approximation theory.


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