Topics In Uniform Approximation Of Continuous Functions

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Topics in Uniform Approximation of Continuous Functions

Author : Ileana Bucur
Publisher : Springer Nature
ISBN 13 : 3030484122
Total Pages : 148 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Topics in Uniform Approximation of Continuous Functions by : Ileana Bucur

Download or read book Topics in Uniform Approximation of Continuous Functions written by Ileana Bucur and published by Springer Nature. This book was released on 2020-08-18 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type. The most important generalizations of Weierstrass’ theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are also included. In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on ¡n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type. The book is intended for advanced and graduate students of mathematics, and can also serve as a resource for researchers in the field of the theory of functions.

Theory of Uniform Approximation of Functions by Polynomials

Author : Vladislav K. Dzyadyk
Publisher : Walter de Gruyter
ISBN 13 : 3110208245
Total Pages : 497 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Theory of Uniform Approximation of Functions by Polynomials by : Vladislav K. Dzyadyk

Download or read book Theory of Uniform Approximation of Functions by Polynomials written by Vladislav K. Dzyadyk and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Approximation Theory and Approximation Practice, Extended Edition

Author : Lloyd N. Trefethen
Publisher : SIAM
ISBN 13 : 1611975948
Total Pages : 377 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Approximation Theory and Approximation Practice, Extended Edition by : Lloyd N. Trefethen

Download or read book Approximation Theory and Approximation Practice, Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.

Theory of Approximation of Functions of a Real Variable

Author : A. F. Timan
Publisher : Elsevier
ISBN 13 : 1483184811
Total Pages : 644 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Theory of Approximation of Functions of a Real Variable by : A. F. Timan

Download or read book Theory of Approximation of Functions of a Real Variable written by A. F. Timan and published by Elsevier. This book was released on 2014-07-22 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Approximation Theory

Author : Harold S. Shapiro
Publisher : Springer
ISBN 13 : 3540364978
Total Pages : 283 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Topics in Approximation Theory by : Harold S. Shapiro

Download or read book Topics in Approximation Theory written by Harold S. Shapiro and published by Springer. This book was released on 2006-11-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Numerical Analysis II

Author : John J.H. Miller
Publisher : Elsevier
ISBN 13 : 032314134X
Total Pages : 281 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Topics in Numerical Analysis II by : John J.H. Miller

Download or read book Topics in Numerical Analysis II written by John J.H. Miller and published by Elsevier. This book was released on 2012-12-02 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Numerical Analysis II contains in complete form, the papers given by the invited speakers to the Conference on Numerical Analysis held under the auspices of the National Committee for Mathematics of the Royal Irish Academy at University College, Dublin from 29th July to 2nd August, 1974. In addition, the titles of the contributed papers are listed together with the names and addresses of the authors who presented them at the conference. This book is divided into 20 chapters that present the papers in their entirety. They discuss such topics as applications of approximation theory to numerical analysis; interior regularity and local convergence of Galerkin finite element approximations for elliptic equations; and numerical estimates for the error of Gauss-Jacobi quadrature formulae. Some remarks on the unified treatment of elementary functions by microprogramming; application of finite difference methods to exploration seismology; and variable coefficient multistep methods for ordinary differential equations applied to parabolic partial differential equations are also presented. Other chapters cover realistic estimates for generic constants in multivariate pointwise approximation; matching of essential boundary conditions in the finite element method; and collocation, difference equations, and stitched function representations. This book will be of interest to practitioners in the fields of mathematics and computer science.

Industrial Information and Design Issues

Author : Jacques-Emile Dubois
Publisher : Springer Science & Business Media
ISBN 13 : 3642802869
Total Pages : 312 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Industrial Information and Design Issues by : Jacques-Emile Dubois

Download or read book Industrial Information and Design Issues written by Jacques-Emile Dubois and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. -E. DUBOIS and N. GERSHON The first volume of this series, "The Information Revolution: Impact on Science and Technology", emphasized the importance of data sharing and fast communication and the advantages l!)f current hypertext developments in creating new and flexible data access. Volume II, "Modeling Complex Data for Creating Information", dealt, in particular, with the specific constraints of science and technology data including imprecision and uncertainty. It also provided representation and handling tools and object oriented programming technology for developing data systems. The papers presented in this third volume are concerned with the very specific information problems of the technical and competitive industrial world. Here, production and selling rely on creative design, information processing, special up-to date data search, knowledge comprehension and fast action, all essential for decision making steps. The following topics are discussed in this volume: • Cognition and Recognition in Design • Knowledge Based Systems (KBS) Evaluation • Modeling Tools for Knowledge Discovery • Standards and CAD (Computer Aided Design) Aspects of Industrial Exchange and Specifications • Information Seeking Strategies of Selective Access to Intelligent Information • Special Information Resources: Complex Databases Most of these topics, inspired by the symposium on "Communication and Computer Aided Systems" held during the 14th International CODATA Conference, deal with systemic components used by various up-to-date industries in development strategies.

Proceedings

Author : Fred Gross
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.:/5 ( download)

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Book Synopsis Proceedings by : Fred Gross

Download or read book Proceedings written by Fred Gross and published by . This book was released on 1971 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uniform Approximations by Trigonometric Polynomials

Author : Alexander I. Stepanets
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110926032
Total Pages : 496 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Uniform Approximations by Trigonometric Polynomials by : Alexander I. Stepanets

Download or read book Uniform Approximations by Trigonometric Polynomials written by Alexander I. Stepanets and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of approximation of functions is one of the central branches in mathematical analysis and has been developed over a number of decades. This monograph deals with a series of problems related to one of the directions of the theory, namely, the approximation of periodic functions by trigonometric polynomials generated by linear methods of summation of Fourier series. More specific, the following linear methods are investigated: classical methods of Fourier, Fejir, Riesz, and Roginski. For these methods the so-called Kolmogorov-Nikol'skii problem is considered, which consists of finding exact and asymptotically exact qualities for the upper bounds of deviations of polynomials generated by given linear methods on given classes of 2?-periodic functions. Much attention is also given to the multidimensional case. The material presented in this monograph did not lose its importance since the publication of the Russian edition (1981). Moreover, new material has been added and several corrections were made. In this field of mathematics numerous deep results were obtained, many important and complicated problems were solved, and new methods were developed, which can be extremely useful for many mathematicians. All principle problems considered in this monograph are given in the final form, i.e. in the form of exact asymptotic equalities, and, therefore, retain their importance and interest for a long time.

Special Topics in Mathematics for Computer Scientists

Author : Ernst-Erich Doberkat
Publisher : Springer
ISBN 13 : 3319227505
Total Pages : 735 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Special Topics in Mathematics for Computer Scientists by : Ernst-Erich Doberkat

Download or read book Special Topics in Mathematics for Computer Scientists written by Ernst-Erich Doberkat and published by Springer. This book was released on 2015-11-16 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems. Using motivations, rigorous definitions, proofs and various examples, the author systematically introduces the Axiom of Choice, explains Banach-Mazur games and the Axiom of Determinacy, discusses the basic constructions of sets and the interplay of coalgebras and Kripke models for modal logics with an emphasis on Kleisli categories, monads and probabilistic systems. The text further shows various ways of defining topologies, building on selected topics like uniform spaces, Gödel’s Completeness Theorem and topological systems. Finally, measurability, general integration, Borel sets and measures on Polish spaces, as well as the coalgebraic side of Markov transition kernels along with applications to probabilistic interpretations of modal logics are presented. Special emphasis is given to the integration of (co-)algebraic and measure-theoretic structures, a fairly new and exciting field, which is demonstrated through the interpretation of game logics. Readers familiar with basic mathematical structures like groups, Boolean algebras and elementary calculus including mathematical induction will discover a wealth of useful research tools. Throughout the book, exercises offer additional information, and case studies give examples of how the techniques can be applied in diverse areas of theoretical computer science and logics. References to the relevant mathematical literature enable the reader to find the original works and classical treatises, while the bibliographic notes at the end of each chapter provide further insights and discussions of alternative approaches.

Toeplitz Approach to Problems of the Uncertainty Principle

Author : Alexei Poltoratski
Publisher : American Mathematical Soc.
ISBN 13 : 1470420171
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Toeplitz Approach to Problems of the Uncertainty Principle by : Alexei Poltoratski

Download or read book Toeplitz Approach to Problems of the Uncertainty Principle written by Alexei Poltoratski and published by American Mathematical Soc.. This book was released on 2015-03-07 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Uncertainty Principle in Harmonic Analysis (UP) is a classical, yet rapidly developing, area of modern mathematics. Its first significant results and open problems date back to the work of Norbert Wiener, Andrei Kolmogorov, Mark Krein and Arne Beurling. At present, it encompasses a large part of mathematics, from Fourier analysis, frames and completeness problems for various systems of functions to spectral problems for differential operators and canonical systems. These notes are devoted to the so-called Toeplitz approach to UP which recently brought solutions to some of the long-standing problems posed by the classics. After a short overview of the general area of UP the discussion turns to the outline of the new approach and its results. Among those are solutions to Beurling's Gap Problem in Fourier analysis, the Type Problem on completeness of exponential systems, a problem by Pólya and Levinson on sampling sets for entire functions, Bernstein's problem on uniform polynomial approximation, problems on asymptotics of Fourier integrals and a Toeplitz version of the Beurling-Malliavin theory. One of the main goals of the book is to present new directions for future research opened by the new approach to the experts and young analysts. A co-publication of the AMS and CBMS.

Analysis of Approximation Methods for Differential and Integral Equations

Author : Hans-Jürgen Reinhardt
Publisher : Springer Science & Business Media
ISBN 13 : 1461210801
Total Pages : 412 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Analysis of Approximation Methods for Differential and Integral Equations by : Hans-Jürgen Reinhardt

Download or read book Analysis of Approximation Methods for Differential and Integral Equations written by Hans-Jürgen Reinhardt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.

Approximation Theory

Author : George Anastassiou
Publisher : CRC Press
ISBN 13 : 9780824787080
Total Pages : 558 pages
Book Rating : 4.7/5 (87 download)

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Book Synopsis Approximation Theory by : George Anastassiou

Download or read book Approximation Theory written by George Anastassiou and published by CRC Press. This book was released on 1992-04-24 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the March 1991 annual conference of the Southeastern Approximation Theorists, in Memphis, Tenn. The 34 papers discuss topics of interest to graduate and professional numerical analysts, applied and industrial mathematicians, engineers, and other scientists such as splines

Selected Topics in Approximation and Computation

Author : Marek A. Kowalski
Publisher : Oxford University Press, USA
ISBN 13 : 0195080599
Total Pages : 366 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Selected Topics in Approximation and Computation by : Marek A. Kowalski

Download or read book Selected Topics in Approximation and Computation written by Marek A. Kowalski and published by Oxford University Press, USA. This book was released on 1995-10-19 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected Topics in Approximation and Computation is a combination of expositions of basic classical methods of approximation leading to popular splines and new explicit tools of computation, including sinc methods, elliptic function methods, and positive operator approximation methods. It also provides an excellent summary of worst case analysis in Information Based Complexity. It relates optimal computational methods e=with the theory of s-numbers and m-widths.

Nonlinear Approximation Theory

Author : Dietrich Braess
Publisher : Springer Science & Business Media
ISBN 13 : 3642616097
Total Pages : 305 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Nonlinear Approximation Theory by : Dietrich Braess

Download or read book Nonlinear Approximation Theory written by Dietrich Braess and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima tion is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly the same time other approaches to nonlinear approximation were also developed. The use of new tools, such as nonlinear functional analysis and topological methods, showed that linearization is not sufficient for a complete treatment of nonlinear families. In particular, the application of global analysis and the consideration of flows on the family of approximating functions intro duced ideas which were previously unknown in approximation theory. These were and still are important in many branches of analysis. On the other hand, methods developed for nonlinear approximation prob lems can often be successfully applied to problems which belong to or arise from linear approximation. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes. The most famous problem of this kind, namely best interpolation by poly nomials, is treated in the appendix of this book.

Introduction to Real Analysis

Author : Manfred Stoll
Publisher : CRC Press
ISBN 13 : 1000345106
Total Pages : 583 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Introduction to Real Analysis by : Manfred Stoll

Download or read book Introduction to Real Analysis written by Manfred Stoll and published by CRC Press. This book was released on 2021-03-09 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition. This text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course, taking into consideration the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student, w hile at the same time challenging the more talented student through the exercises. Chapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters, the theorems, examples, and exercises require greater sophistication and mathematical maturity for full understanding. In addition to the standard topics the text includes topics that are not always included in comparable texts. Chapter 6 contains a section on the Riemann-Stieltjes integral and a proof of Lebesgue’s t heorem providing necessary and sufficient conditions for Riemann integrability. Chapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces. C hapter 8 contains a proof of the Weierstrass approximation theorem using the method of aapproximate identities. The inclusion of Fourier series in the text allows the student to gain some exposure to this important subject. The final chapter includes a detailed treatment of Lebesgue measure and the Lebesgue integral, using inner and outer measure. The exercises at the end of each section reinforce the concepts. Notes provide historical comments or discuss additional topics.