On The Degree Of Approximation Of Continuous Functions By Positive Linear Operators
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The Approximation Of Continuous Functions By Positive Linear Operators
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Author : Ronald A. De Vore
language : en
Publisher: Springer
Release Date : 2006-11-15
The Approximation Of Continuous Functions By Positive Linear Operators written by Ronald A. De Vore and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
On The Degree Of Approximation Of Continuous Functions By Positive Linear Operators
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Author : Jovan Karamata
language : en
Publisher:
Release Date : 1964
On The Degree Of Approximation Of Continuous Functions By Positive Linear Operators written by Jovan Karamata and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Functions, Continuous categories.
A theorem of B. Bajsanski and R. Bojanic ('A note on approximation by Bernstein polynomials.' Bull. Amer. Math. Soc. 70(1964), p. 675-677) is extended to general linear positive operators. (Author).
Approximation Theory Using Positive Linear Operators
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Author : Radu Paltanea
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximation Theory Using Positive Linear Operators written by Radu Paltanea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
We deal in this work with quantitative results in the pointwise approximation of func tions by positive linear functionals and operators. One of the main objectives is to obtain estimates for the degree of approximation in terms of various types of second order moduli of continuity. In the category of sec ond order moduli we include both classical and newly introduced moduli. Particular attention is paid to optimizing the constants appearing in such estimates. In the last decades, the study of linear positive operators with the aid of second order moduli was intensive, thanks to their refinements in characterization of the smoothness of functions. As promoters of this direction of research we mention Yu. Brudnyi, G. Freud, and J. Petree. Our approach is more akin to the approach taken by H. Gonska, who obtained the first general estimates for second order moduli with precise constants and with free parameters. Two new methods will be presented. The first one, based on decomposition of functionals and the use of moments, can be applied to diverse types of moduli and leads to simple estimates. The second method gives sufficient conditions for obtaining absolute optimal constants. The benefits of these more direct methods, compared with the known method based on K-functionals, consist in the improvement and even the optimization of the constants, and in the generalization of the framework.
Linear Operators And Approximation Lineare Operatoren Und Approximation
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Author : Bautzer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Linear Operators And Approximation Lineare Operatoren Und Approximation written by Bautzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research In stitute, August 14-22, 1971. There were thirty-eight such lectures while four addi tional papers, subsequently submitted in writing, are also included in this volume. Two of the three lectures presented by Russian mathematicians are rendered in English, the third in Russian. Furthermore, there is areport on new and unsolved problems based upon special problem sessions, with later communications from the participants. In fact, two of the papers inc1uded are devoted to solutions of some of the problems posed. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily somewhat arbitrary. Thus Chapter I on Operator Theory is concerned with linear and non linear semi-groups, structure of single operators, unitary operators, spectral and ergodic theory. Chapter Il on Topics in Functional Analysis inc1udes papers on Riesz spaces, boundedness theorems, generalized limits, and distributions. Chapter III, entitled "Approximation in Abstract Spaces", ranges from characterizations of c1asses of functions in approximation theory to approximation-theoretical topics connected with extensions to Banach (or more general) spaces. Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation. A large part of the general editorial work connected with these proceedings was competently handled by Miss F. Feber, while G.
Convergence Estimates In Approximation Theory
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Author : Vijay Gupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-08
Convergence Estimates In Approximation Theory written by Vijay Gupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.
The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.
Fuzzy Mathematics Approximation Theory
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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-15
Fuzzy Mathematics Approximation Theory written by George A. Anastassiou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-15 with Computers categories.
This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and the topics covered are very diverse. An extensive background of Fuzziness and Fuzzy Real Analysis is given. The author covers Fuzzy Differentiation and Integration Theory followed by Fuzzy Ostrowski inequalities. Then results on classical algebraic and trigonometric polynomial Fuzzy Approximation are presented. The author develops a complete theory of convergence with rates of Fuzzy Positive linear operators to Fuzzy unit operator, the so-called Fuzzy Korovkin Theory. The related Fuzzy Global Smoothness is included. Then follows the study of Fuzzy Wavelet type operators and their convergence with rates to Fuzzy unit operator. Similarly the Fuzzy Neural Network Operators are discussed followed by Fuzzy Random Korovkin approximation theory and Fuzzy Random Neural Network approximations. The author continues with Fuzzy Korovkin approximations in the sense of Summability. Finally fuzzy sense differences of Fuzzy Wavelet type operators are estimated. The monograph's approach is quantitative and the main results are given via Fuzzy inequalities, involving Fuzzy moduli of continuity, that is Fuzzy Jackson type inequalities. The exposed theory is destined and expected to find applications to all aspects of Fuzziness from theoretical to practical in almost all sciences, technology, finance and industry. Also it has its interest within Pure Mathematics. So this monograph is suitable for researchers, graduate students and seminars of theoretical and applied mathematics, computer science, statistics and engineering.
Approximation With Positive Linear Operators And Linear Combinations
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Author : Vijay Gupta
language : en
Publisher: Springer
Release Date : 2017-06-27
Approximation With Positive Linear Operators And Linear Combinations written by Vijay Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-27 with Mathematics categories.
This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
Spline Functions Basic Theory
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Author : Larry Schumaker
language : en
Publisher: Cambridge University Press
Release Date : 2007-08-16
Spline Functions Basic Theory written by Larry Schumaker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-16 with Mathematics categories.
This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.
Technical Abstract Bulletin
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Author :
language : en
Publisher:
Release Date :
Technical Abstract Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
Korovkin Type Approximation Theory And Its Applications
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Author : Francesco Altomare
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-21
Korovkin Type Approximation Theory And Its Applications written by Francesco Altomare and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-21 with Mathematics categories.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.