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Author: James L. Tyler
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: James L. Tyler
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: Le Baron O. Ferguson
Publisher: American Mathematical Soc.
ISBN: 0821815172
Category : Mathematics
Languages : en
Pages : 174
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Book Description
Addresses two questions that include: 'What functions can be approximated by polynomials whose coefficients are integers?' and 'How well are they approximated (Jackson type theorems)?'
Author: V. K. Dzyadyk
Publisher: VSP
ISBN: 9789067641944
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This book is the result of 20 years of investigations carried out by the author and his colleagues in order to bring closer and, to a certain extent, synthesize a number of well-known results, ideas and methods from the theory of function approximation, theory of differential and integral equations and numerical analysis. The book opens with an introduction on the theory of function approximation and is followed by a new approach to the Fredholm integral equations to the second kind. Several chapters are devoted to the construction of new methods for the effective approximation of solutions of several important integral, and ordinary and partial differential equations. In addition, new general results on the theory of linear differential equations with one regular singular point, as well as applications of the various new methods are discussed.
Author: A. F. Timan
Publisher: Elsevier
ISBN: 1483184811
Category : Mathematics
Languages : en
Pages : 644
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Book Description
Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.
Author: Ronald A. De Vore
Publisher: Springer
ISBN: 3540379959
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Author: Theodore J. Rivlin
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 168
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Book Description
Approximation theory is an area of mathematics with important practical applications in computation. This volume provides an introduction to the theoretical foundations which underlie many of the algorithms of everyday use. For each method of approximation studied, at least one algorithm leading to actual numerical approximations is described.
Author: Peter Junghanns
Publisher: Springer Nature
ISBN: 303077497X
Category : Mathematics
Languages : en
Pages : 662
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Book Description
The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
Author: G. G. Lorentz
Publisher: American Mathematical Society
ISBN: 1470474948
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This is an easily accessible account of the approximation of functions. It is simple and without unnecessary details, but complete enough to include the classical results of the theory. With only a few exceptions, only functions of one real variable are considered. A major theme is the degree of uniform approximation by linear sets of functions. This encompasses approximations by trigonometric polynomials, algebraic polynomials, rational functions, and polynomial operators. The chapter on approximation by operators does not assume extensive knowledge of functional analysis. Two chapters cover the important topics of widths and entropy. The last chapter covers the solution by Kolmogorov and Arnol?d of Hilbert's 13th problem. There are notes at the end of each chapter that give information about important topics not treated in the main text. Each chapter also has a short set of challenging problems, which serve as illustrations.
Author: Vladislav K. Dzyadyk
Publisher: Walter de Gruyter
ISBN: 3110208245
Category : Mathematics
Languages : en
Pages : 497
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Book Description
A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms. The topics include Chebychev theory, Weierstraß theorems, smoothness of functions, and continuation of functions.
Author: H N Mhaskar
Publisher: World Scientific
ISBN: 9814518050
Category : Mathematics
Languages : en
Pages : 398
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Book Description
In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.
