Progress In Approximation Theory

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Progress in Approximation Theory and Applicable Complex Analysis

Author : Narendra Kumar Govil
Publisher : Springer
ISBN 13 : 9783319841120
Total Pages : 519 pages
Book Rating : 4.8/5 (411 download)

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Book Synopsis Progress in Approximation Theory and Applicable Complex Analysis by : Narendra Kumar Govil

Download or read book Progress in Approximation Theory and Applicable Complex Analysis written by Narendra Kumar Govil and published by Springer. This book was released on 2018-07-20 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Progress in Approximation Theory

Author : A.A. Gonchar
Publisher : Springer Science & Business Media
ISBN 13 : 1461229669
Total Pages : 463 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Progress in Approximation Theory by : A.A. Gonchar

Download or read book Progress in Approximation Theory written by A.A. Gonchar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.

Progress in Approximation Theory

Author : Paul G. Nevai
Publisher :
ISBN 13 :
Total Pages : 936 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Progress in Approximation Theory by : Paul G. Nevai

Download or read book Progress in Approximation Theory written by Paul G. Nevai and published by . This book was released on 1991 with total page 936 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Progress in Approximation Theory and Applicable Complex Analysis

Author : Narendra Kumar Govil
Publisher : Springer
ISBN 13 : 331949242X
Total Pages : 519 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Progress in Approximation Theory and Applicable Complex Analysis by : Narendra Kumar Govil

Download or read book Progress in Approximation Theory and Applicable Complex Analysis written by Narendra Kumar Govil and published by Springer. This book was released on 2017-04-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Progress in Approximation Theory

Author : A. A. Gonchar
Publisher :
ISBN 13 : 9781461229674
Total Pages : 476 pages
Book Rating : 4.2/5 (296 download)

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Book Synopsis Progress in Approximation Theory by : A. A. Gonchar

Download or read book Progress in Approximation Theory written by A. A. Gonchar and published by . This book was released on 1992-11-01 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Progress in Approximation Theory

Author : A.A. Gonchar
Publisher : Springer
ISBN 13 : 9780387979014
Total Pages : 451 pages
Book Rating : 4.9/5 (79 download)

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Book Synopsis Progress in Approximation Theory by : A.A. Gonchar

Download or read book Progress in Approximation Theory written by A.A. Gonchar and published by Springer. This book was released on 1992-11-12 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.

New Developments in Approximation Theory

Author : Manfred W. Müller
Publisher : Springer Science & Business Media
ISBN 13 : 9783764361433
Total Pages : 352 pages
Book Rating : 4.3/5 (614 download)

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Book Synopsis New Developments in Approximation Theory by : Manfred W. Müller

Download or read book New Developments in Approximation Theory written by Manfred W. Müller and published by Springer Science & Business Media. This book was released on 1999 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains refereed papers which were presented at the Second International Dortmund Meeting on Approximation Theory (IDoMAT '98) at Haus Bommerholz, the conference center of Dortmund University, during the week of February 23-27, 1998. At this conference 50 researchers and specialists from Bulgaria, China, France, Great Britain, Hungary, Israel, Italy, Romania, South Africa and Germany participated and described new developments in the fields of univariate and multivariate approximation theory. The papers cover topics such as radial basis functions, bivariate spline interpolation, subdivision algorithms, multilevel interpolation, multivariate triangular Bernstein bases, Padè approximation, comonotone polynomial approximation, weighted and unweighted polynomial approximation, adaptive approximation, approximation operators of binomial type, quasi-interpolants, generalized convexity and Peano kernel techniques.This research has applications in areas such as computer-aided geometric design, as applied in engineering and medical technology (e.g. computerized tomography).

Advances in Applied Mathematics and Approximation Theory

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
ISBN 13 : 1461463939
Total Pages : 486 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Advances in Applied Mathematics and Approximation Theory by : George A. Anastassiou

Download or read book Advances in Applied Mathematics and Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at “Applied Mathematics and Approximation Theory 2012,” an international conference held in Ankara, Turkey, May 17-20, 2012. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. The collection will be a useful resource for researchers in applied mathematics, engineering and statistics.

Recent Advances in Constructive Approximation Theory

Author : Vijay Gupta
Publisher : Springer
ISBN 13 : 9783030063740
Total Pages : 304 pages
Book Rating : 4.0/5 (637 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 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.

Advances in Summability and Approximation Theory

Author : S. A. Mohiuddine
Publisher : Springer
ISBN 13 : 9811330778
Total Pages : 241 pages
Book Rating : 4.8/5 (113 download)

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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.

Theory of Approximation

Author : N. I. Achieser
Publisher : Courier Corporation
ISBN 13 : 0486153134
Total Pages : 324 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Theory of Approximation by : N. I. Achieser

Download or read book Theory of Approximation written by N. I. Achieser and published by Courier Corporation. This book was released on 2013-06-05 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).

Approximation Theory

Author : Narenda Govil
Publisher : CRC Press
ISBN 13 : 9780824701857
Total Pages : 560 pages
Book Rating : 4.7/5 (18 download)

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Book Synopsis Approximation Theory by : Narenda Govil

Download or read book Approximation Theory written by Narenda Govil and published by CRC Press. This book was released on 1998-05-12 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

Approximation Theory

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641511
Total Pages : 554 pages
Book Rating : 4.6/5 (415 download)

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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 1999-12-22 with total page 554 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.

Korovkin-type Approximation Theory and Its Applications

Author : Francesco Altomare
Publisher : Walter de Gruyter
ISBN 13 : 3110884585
Total Pages : 641 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Korovkin-type Approximation Theory and Its Applications by : Francesco Altomare

Download or read book Korovkin-type Approximation Theory and Its Applications written by Francesco Altomare and published by Walter de Gruyter. This book was released on 2011-07-21 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Progress in Multivariate Approximation

Author : Werner Haussmann
Publisher : Birkhäuser
ISBN 13 : 3034882726
Total Pages : 258 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Recent Progress in Multivariate Approximation by : Werner Haussmann

Download or read book Recent Progress in Multivariate Approximation written by Werner Haussmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. An essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.

Approximation Theory and Harmonic Analysis on Spheres and Balls

Author : Feng Dai
Publisher : Springer Science & Business Media
ISBN 13 : 1461466601
Total Pages : 447 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Approximation Theory and Harmonic Analysis on Spheres and Balls by : Feng Dai

Download or read book Approximation Theory and Harmonic Analysis on Spheres and Balls written by Feng Dai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Approximation Theory XIII: San Antonio 2010

Author : Marian Neamtu
Publisher : Springer Science & Business Media
ISBN 13 : 1461407729
Total Pages : 418 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Approximation Theory XIII: San Antonio 2010 by : Marian Neamtu

Download or read book Approximation Theory XIII: San Antonio 2010 written by Marian Neamtu and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007). Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.