Recent Advances In Constructive Approximation Theory

Author : Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal
Publisher : Springer
Page : 304 pages
File Size : 47,6 Mb
Release : 2019-08
Category : Electronic
ISBN : 3030063747

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Recent Advances in Constructive Approximation Theory by Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal Pdf

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 : Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal,Ana Maria Acu
Publisher : Springer
Page : 291 pages
File Size : 44,6 Mb
Release : 2018-07-06
Category : Mathematics
ISBN : 9783319921655

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Recent Advances in Constructive Approximation Theory by Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal,Ana Maria Acu Pdf

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 : Ronald A. DeVore,George G. Lorentz
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 46,6 Mb
Release : 1993-11-04
Category : Mathematics
ISBN : 3540506276

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Constructive Approximation by Ronald A. DeVore,George G. Lorentz Pdf

Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.

Author : George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz
Publisher : Springer
Page : 649 pages
File Size : 47,5 Mb
Release : 1996
Category : Mathematics
ISBN : 3642609325

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Constructive Approximation by George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz Pdf

In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Author : Martin D. Buhmann,Detlef Mache
Publisher : Birkhäuser
Page : 286 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034876001

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Advanced Problems in Constructive Approximation by Martin D. Buhmann,Detlef Mache Pdf

The current form of modern approximation theory is shaped by many new de velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approxima tion order and error estimates, as well as constructions of function systems for approximation of functions on Euclidean spaces and spheres. It is a piece of very good fortune that at all of the IDoMAT meetings, col leagues and friends from all over Europe, and indeed some count ries outside Europe and as far away as China, New Zealand, South Africa and U.S.A. came and dis cussed mathematics at IDoMAT conference facility in Witten-Bommerholz. The conference was, as always, held in a friendly and congenial atmosphere. After each meeting, the delegat es were invited to contribute to the proceed ing's volume, the previous one being published in the same Birkhäuser series as this one. The editors were pleased about the quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their work.

Author : Detlef H. Mache,József Szabados,Marcel G. de Bruin
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 50,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373566

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Trends and Applications in Constructive Approximation by Detlef H. Mache,József Szabados,Marcel G. de Bruin Pdf

This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.

Author : George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz
Publisher : Springer
Page : 0 pages
File Size : 44,9 Mb
Release : 2011-12-21
Category : Mathematics
ISBN : 3642646107

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Constructive Approximation by George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz Pdf

In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Author : George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz
Publisher : Springer
Page : 674 pages
File Size : 44,9 Mb
Release : 1996-05-14
Category : Mathematics
ISBN : UCSD:31822021497052

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Constructive Approximation by George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz Pdf

In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Author : Armin Iske
Publisher : Springer
Page : 358 pages
File Size : 45,7 Mb
Release : 2018-12-14
Category : Mathematics
ISBN : 9783030052287

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Approximation Theory and Algorithms for Data Analysis by Armin Iske Pdf

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.

Author : Andrei A. Gonchar,Edward B. Saff
Publisher : Springer
Page : 225 pages
File Size : 49,9 Mb
Release : 2008-01-03
Category : Mathematics
ISBN : 9783540477921

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Methods of Approximation Theory in Complex Analysis and Mathematical Physics by Andrei A. Gonchar,Edward B. Saff Pdf

The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. Suslov: Classical Biorthogonal Rational Functions.- V.P. Havin, A. Presa Sague: Approximation properties of harmonic vector fields and differential forms.- O.G. Parfenov: Extremal problems for Blaschke products and N-widths.- A.J. Carpenter, R.S. Varga: Some Numerical Results on Best Uniform Polynomial Approximation of x on 0,1 .- J.S. Geronimo: Polynomials Orthogonal on the Unit Circle with Random Recurrence Coefficients.- S. Khrushchev: Parameters of orthogonal polynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.

Author : Werner Haussmann,Kurt Jetter,Manfred Reimer
Publisher : Birkhäuser
Page : 258 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882729

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Recent Progress in Multivariate Approximation by Werner Haussmann,Kurt Jetter,Manfred Reimer Pdf

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.

Author : Karl-Georg Steffens
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 43,7 Mb
Release : 2007-07-28
Category : Mathematics
ISBN : 9780817644758

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The History of Approximation Theory by Karl-Georg Steffens Pdf

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation

Author : S. A. Mohiuddine,Tuncer Acar
Publisher : Springer
Page : 241 pages
File Size : 51,7 Mb
Release : 2018-12-30
Category : Mathematics
ISBN : 9789811330773

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Advances in Summability and Approximation Theory by S. A. Mohiuddine,Tuncer Acar Pdf

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.

Author : Marian Neamtu,E. B. Saff
Publisher : Unknown
Page : 552 pages
File Size : 42,9 Mb
Release : 2004
Category : Mathematics
ISBN : UOM:39015063279627

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Advances in Constructive Approximation by Marian Neamtu,E. B. Saff Pdf

Author : Barnabás Bede,Lucian Coroianu,Sorin G. Gal
Publisher : Springer
Page : 458 pages
File Size : 55,5 Mb
Release : 2016-08-08
Category : Mathematics
ISBN : 9783319341897

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Approximation by Max-Product Type Operators by Barnabás Bede,Lucian Coroianu,Sorin G. Gal Pdf

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.