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Approximation Theory Using Positive Linear Operators
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Book Synopsis Approximation Theory Using Positive Linear Operators by : Radu Paltanea
Download or read book Approximation Theory Using Positive Linear Operators written by Radu Paltanea and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results
Book Synopsis Approximation with Positive Linear Operators and Linear Combinations by : Vijay Gupta
Download or read book Approximation with Positive Linear Operators and Linear Combinations written by Vijay Gupta and published by Springer. This book was released on 2017-06-27 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Approximation of Continuous Functions by Positive Linear Operators by : Ronald A. De Vore
Download or read book The Approximation of Continuous Functions by Positive Linear Operators written by Ronald A. De Vore and published by Springer. This book was released on 2006-11-15 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Moments of Linear Positive Operators and Approximation by : Vijay Gupta
Download or read book Moments of Linear Positive Operators and Approximation written by Vijay Gupta and published by Springer. This book was released on 2019-05-25 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.
Book Synopsis The Approximation of Continuous Functions by Positive Linear Operators by : Ronald A. De Vore
Download or read book The Approximation of Continuous Functions by Positive Linear Operators written by Ronald A. De Vore and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Advances in Constructive Approximation Theory by : Vijay Gupta
Download or read book Recent Advances in Constructive Approximation Theory written by Vijay Gupta and published by Springer. This book was released on 2018-07-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.
Book Synopsis Recent Advances in Constructive Approximation Theory by : Vijay Gupta
Download or read book Recent Advances in Constructive Approximation Theory written by Vijay Gupta and published by Springer. This book was released on 2019-08 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type convergence of GBS operators.
Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :1461213606 Total Pages :520 pages Book Rating :4.4/5 (612 download)
Book Synopsis Approximation Theory by : George A. Anastassiou
Download or read book Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear Operators and Approximation Theory by : Pavel Petrovich Korovkin
Download or read book Linear Operators and Approximation Theory written by Pavel Petrovich Korovkin and published by . This book was released on 1960 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence Estimates in Approximation Theory by : Vijay Gupta
Download or read book Convergence Estimates in Approximation Theory written by Vijay Gupta and published by Springer Science & Business Media. This book was released on 2014-01-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications of q-Calculus in Operator Theory by : Ali Aral
Download or read book Applications of q-Calculus in Operator Theory written by Ali Aral and published by Springer Science & Business Media. This book was released on 2013-05-09 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.
Book Synopsis Computation and Approximation by : Vijay Gupta
Download or read book Computation and Approximation written by Vijay Gupta and published by Springer Nature. This book was released on 2021-11-29 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators. It will be of interest to students both graduate and undergraduate studying linear positive operators and the area of approximation theory.
Book Synopsis Approximation Theory, Sequence Spaces and Applications by : S. A. Mohiuddine
Download or read book Approximation Theory, Sequence Spaces and Applications written by S. A. Mohiuddine and published by Springer Nature. This book was released on 2022-12-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
Book Synopsis Advances in Summability and Approximation Theory by : S. A. Mohiuddine
Download or read book Advances in Summability and Approximation Theory written by S. A. Mohiuddine and published by Springer. This book was released on 2018-12-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.
Book Synopsis Quantitative Estimates for Certain Positive Linear Operators by : Gunjan Agarwal
Download or read book Quantitative Estimates for Certain Positive Linear Operators written by Gunjan Agarwal and published by . This book was released on 2024-01-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The convergence behaviour of linear positive operators has been a prominent topic and many scholars have investigated it using a variety of methodologies for exactness. Approx- imation theory is primarily concerned with the investigation of several direct results such as the asymptotic formula, point-wise convergence and error estimates in simultaneous and ordinary approximation. These findings are necessary from a convergence standpoint. Dun- ham Jackson [103] proved algebraic and trigonometric polynomial direct theorems. Profes- sor Edmund Georg Hermann Landau, Jackson's supervisor, was the one who came up with the Big-O and small-o symbols. The asymptotic behaviour of a function is represented by these symbols. Because a function's rate of growth is known as its order, the letter 'O' or 'o' is utilised. As a result, the order of approximation is represented by these symbols. The crucial theorem proved by Weierstrass in 1885 made it possible to study some sorts of complicated functions by a simpler function with a suitable rate of approximation. Thus, linear positive operator approximation theory is based mostly on the "Weierstrass approxima- tion theorem," which states that "every continuous function defined on a closed and bounded interval may be uniformly approximated by a polynomial". Polynomials are among the most basic functions and computers can instantly evaluate polynomials. The Bernstein polyno- mials are used in the most typical proof of this well-known theorem. Additionally, Borislav Dechev Boyanov [33] was one of the pioneers in the field of mathematics to demonstrate the presence and originality of answers to numerous issues pertaining to approximation the- ory. Academician Blagovest Hristov Sendov, who served as his supervisor, visited Moscow State University in the early 1960s as new, interesting fields in approximation theory began to emerge. During this time, Sergei Natanovich Bernstein was still engaged in mathematical studies.
Author :Vladimir Ya. Eiderman Publisher :Springer Science & Business Media ISBN 13 :3764373407 Total Pages :225 pages Book Rating :4.7/5 (643 download)
Book Synopsis Selected Topics in Complex Analysis by : Vladimir Ya. Eiderman
Download or read book Selected Topics in Complex Analysis written by Vladimir Ya. Eiderman and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.
Book Synopsis Markov Operators, Positive Semigroups and Approximation Processes by : Francesco Altomare
Download or read book Markov Operators, Positive Semigroups and Approximation Processes written by Francesco Altomare and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-12-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.
