Bernstein Operators And Their Properties

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Bernstein Operators and Their Properties

Author : Jorge Bustamante
Publisher : Birkhäuser
ISBN 13 : 3319554026
Total Pages : 423 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Bernstein Operators and Their Properties by : Jorge Bustamante

Download or read book Bernstein Operators and Their Properties written by Jorge Bustamante and published by Birkhäuser. This book was released on 2017-04-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties. This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter. The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.

Moduli of Smoothness

Author : Z. Ditzian
Publisher : Springer Science & Business Media
ISBN 13 : 1461247780
Total Pages : 233 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Moduli of Smoothness by : Z. Ditzian

Download or read book Moduli of Smoothness written by Z. Ditzian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the introduction and application of a new measure for smoothness offunctions. Though we have both previously published some articles in this direction, the results given here are new. Much of the work was done in the summer of 1984 in Edmonton when we consolidated earlier ideas and worked out most of the details of the text. It took another year and a half to improve and polish many of the theorems. We express our gratitude to Paul Nevai and Richard Varga for their encouragement. We thank NSERC of Canada for its valuable support. We also thank Christine Fischer and Laura Heiland for their careful typing of our manuscript. z. Ditzian V. Totik CONTENTS Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 PART I. THE MODULUS OF SMOOTHNESS Chapter 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1. Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2. Discussion of Some Conditions on cp(x). . . . • . . . . . . . • . . • . . • • . 8 . . . • . 1.3. Examples of Various Step-Weight Functions cp(x) . . • . . • . . • . . • . . . 9 . . • Chapter 2. The K-Functional and the Modulus of Continuity ... . ... 10 2.1. The Equivalence Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . 2.2. The Upper Estimate, Kr.tp(f, tr)p ~ Mw;(f, t)p, Case I . . . . . . . . . . . . 12 . . . 2.3. The Upper Estimate of the K-Functional, The Other Cases. . . . . . . . . . 16 . 2.4. The Lower Estimate for the K-Functional. . . . . . . . . . . . . . . . . . . 20 . . . . . Chapter 3. K-Functionals and Moduli of Smoothness, Other Forms. 24 3.1. A Modified K-Functional . . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . 3.2. Forward and Backward Differences. . . . . . . . . . . . . . . . . . . . . . 26 . . . . . . . 3.3. Main-Part Modulus of Smoothness. . . . . . . . . . . . . . . . . . . . . . 28 . . . . . . .

Approximation By Complex Bernstein And Convolution Type Operators

Author : Sorin G Gal
Publisher : World Scientific
ISBN 13 : 9814466972
Total Pages : 350 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Approximation By Complex Bernstein And Convolution Type Operators by : Sorin G Gal

Download or read book Approximation By Complex Bernstein And Convolution Type Operators written by Sorin G Gal and published by World Scientific. This book was released on 2009-08-11 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.

Arc Schemes And Singularities

Author : David Bourqui
Publisher : World Scientific
ISBN 13 : 1786347210
Total Pages : 312 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Arc Schemes And Singularities by : David Bourqui

Download or read book Arc Schemes And Singularities written by David Bourqui and published by World Scientific. This book was released on 2020-03-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.

Approximation by Max-Product Type Operators

Author : Barnabás Bede
Publisher : Springer
ISBN 13 : 3319341898
Total Pages : 468 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Approximation by Max-Product Type Operators by : Barnabás Bede

Download or read book Approximation by Max-Product Type Operators written by Barnabás Bede and published by Springer. This book was released on 2016-08-08 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Analysis

Author : Andrew R. Mitchell
Publisher : World Scientific
ISBN 13 : 9789810227197
Total Pages : 384 pages
Book Rating : 4.2/5 (271 download)

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Book Synopsis Numerical Analysis by : Andrew R. Mitchell

Download or read book Numerical Analysis written by Andrew R. Mitchell and published by World Scientific. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.

Quantum Calculus

Author : Victor Kac
Publisher : Springer Science & Business Media
ISBN 13 : 1461300711
Total Pages : 121 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Quantum Calculus by : Victor Kac

Download or read book Quantum Calculus written by Victor Kac and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.

Bernstein Polynomials

Author : G. G. Lorentz
Publisher : American Mathematical Soc.
ISBN 13 : 0821875582
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Bernstein Polynomials by : G. G. Lorentz

Download or read book Bernstein Polynomials written by G. G. Lorentz and published by American Mathematical Soc.. This book was released on 2012 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernstein polynomials are a remarkable family of polynomials associated to any given function on the unit interval. Their first notable appearance was in Bernstein's proof of the Weierstrass approximation theorem. This book gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in analysis. The first three chapters of the book give an introduction to a theory of singular integrals by means of the particular instance of Bernstein polynomials. The author writes in the preface to this second edition, "After the trigonometric integrals, Bernstein polynomials are the most important and interesting concrete operators on a space of continuous functions. Since the appearance of the first edition of this book [in 1953], the interest in this subject has continued. In an appendix we have summed up a few of the most important papers that have appeared since."

An Introduction to the Approximation of Functions

Author : Theodore J. Rivlin
Publisher : Courier Corporation
ISBN 13 : 9780486640693
Total Pages : 164 pages
Book Rating : 4.6/5 (46 download)

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Book Synopsis An Introduction to the Approximation of Functions by : Theodore J. Rivlin

Download or read book An Introduction to the Approximation of Functions written by Theodore J. Rivlin and published by Courier Corporation. This book was released on 1981-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Mathematical Methods in Engineering

Author : Nuno Miguel Fonseca Ferreira
Publisher : Springer
ISBN 13 : 9400771835
Total Pages : 311 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Mathematical Methods in Engineering by : Nuno Miguel Fonseca Ferreira

Download or read book Mathematical Methods in Engineering written by Nuno Miguel Fonseca Ferreira and published by Springer. This book was released on 2014-08-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.

Approximation Theory Using Positive Linear Operators

Author : Radu Paltanea
Publisher : Springer Science & Business Media
ISBN 13 : 1461220580
Total Pages : 208 pages
Book Rating : 4.4/5 (612 download)

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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

Scientific Support for the Decision Making in the Security Sector

Author : Ognyan Kounchev
Publisher : IOS Press
ISBN 13 : 1586037609
Total Pages : 360 pages
Book Rating : 4.5/5 (86 download)

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Book Synopsis Scientific Support for the Decision Making in the Security Sector by : Ognyan Kounchev

Download or read book Scientific Support for the Decision Making in the Security Sector written by Ognyan Kounchev and published by IOS Press. This book was released on 2007 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Security environment is characterized by deep uncertainty. Threats are being posed not only by adversary (political) forces but may also come from natural challenges. This title reflects the initial state of a dialogue between specialists in security and specialists in mathematics, computer and information sciences on security topics.

Approximation of Functions: Theory and Numerical Methods

Author : Günter Meinardus
Publisher : Springer Science & Business Media
ISBN 13 : 3642856438
Total Pages : 207 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Approximation of Functions: Theory and Numerical Methods by : Günter Meinardus

Download or read book Approximation of Functions: Theory and Numerical Methods written by Günter Meinardus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: for example, the so-called Lp approximation, the Bernstein approxima tion problem (approximation on the real line by certain entire functions), and the highly interesting studies of J. L. WALSH on approximation in the complex plane. I would like to extend sincere thanks to Professor L. COLLATZ for his many encouragements for the writing of this book. Thanks are equally due to Springer-Verlag for their ready agreement to my wishes, and for the excellent and competent composition of the book. In addition, I would like to thank Dr. W. KRABS, Dr. A. -G. MEYER and D. SCHWEDT for their very careful reading of the manuscript. Hamburg, March 1964 GUNTER MEINARDUS Preface to the English Edition This English edition was translated by Dr. LARRY SCHUMAKER, Mathematics Research Center, United States Army, The University of Wisconsin, Madison, from a supplemented version of the German edition. Apart from a number of minor additions and corrections and a few new proofs (e. g. , the new proof of JACKSON'S Theorem), it differs in detail from the first edition by the inclusion of a discussion of new work on comparison theorems in the case of so-called regular Haar systems (§ 6) and on Segment Approximation (§ 11). I want to thank the many readers who provided comments and helpful suggestions. My special thanks are due to the translator, to Springer-Verlag for their ready compliance with all my wishes, to Mr.

Applications of q-Calculus in Operator Theory

Author : Ali Aral
Publisher : Springer Science & Business Media
ISBN 13 : 1461469465
Total Pages : 275 pages
Book Rating : 4.4/5 (614 download)

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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.

Current Trends in Symmetric Polynomials with their Applications

Author : Taekyun Kim
Publisher : MDPI
ISBN 13 : 3039216201
Total Pages : 238 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Current Trends in Symmetric Polynomials with their Applications by : Taekyun Kim

Download or read book Current Trends in Symmetric Polynomials with their Applications written by Taekyun Kim and published by MDPI. This book was released on 2019-10-15 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Recent Advances in Constructive Approximation Theory

Author : Vijay Gupta
Publisher : Springer
ISBN 13 : 3319921657
Total Pages : 295 pages
Book Rating : 4.3/5 (199 download)

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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 295 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.

Fuzzy Systems & Operations Research and Management

Author : Bing-Yuan Cao
Publisher : Springer
ISBN 13 : 3319191055
Total Pages : 402 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Fuzzy Systems & Operations Research and Management by : Bing-Yuan Cao

Download or read book Fuzzy Systems & Operations Research and Management written by Bing-Yuan Cao and published by Springer. This book was released on 2015-07-31 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes results of the seventh International Conference on Fuzzy Information and Engineering (ICFIE'2014) and the 1st International Conference of Operations Research and Management (ICORM'2014) on November 7-11, 2014 in ZhuHai, China. The book, contains 35 selected high-quality papers, and is divided into five main parts: Part I focuses on ``Fuzzy Systems and Its Applications", Part II on ``Fuzzy Mathematics and Its Applications", Part III discusses ``Fuzzy Information and Computer", Part IV is devoted to ``Operations Research and Management and Its Applications" and Part V includes various other topics.