N Widths In Approximation Theory

Author : A. Pinkus
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642698941

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n-Widths in Approximation Theory by A. Pinkus Pdf

My original introduction to this subject was through conservations, and ultimate ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction . . . . . . . . Chapter II. Basic Properties of n-Widths . 9 1. Properties of d • • • • • • • • • • 9 n 15 2. Existence of Optimal Subspaces for d • n n 17 3. Properties of d • • • • • • 20 4. Properties of b • • • • • • n 5. Inequalities Between n-Widths 22 n 6. Duality Between d and d • • 27 n 7. n-Widths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References . . . . . . . . . . . . . .

Author : A Pinkus
Publisher : Unknown
Page : 308 pages
File Size : 40,5 Mb
Release : 1984-12-01
Category : Electronic
ISBN : 3642698956

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N-Widths in Approximation Theory by A Pinkus Pdf

Author : Andrei A. Gonchar,Edward B. Saff
Publisher : Springer
Page : 225 pages
File Size : 47,8 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 : Nikolaĭ Pavlovich Korneĭchuk
Publisher : Cambridge University Press
Page : 472 pages
File Size : 44,9 Mb
Release : 1991-06-06
Category : Mathematics
ISBN : 0521382343

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Exact Constants in Approximation Theory by Nikolaĭ Pavlovich Korneĭchuk Pdf

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.

Author : Carl De Boor,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 42,5 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 0821867431

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Approximation Theory by Carl De Boor,American Mathematical Society Pdf

The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, $N$-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics. The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra.

Author : A. Pinkus
Publisher : Springer
Page : 312 pages
File Size : 43,8 Mb
Release : 1985
Category : Language Arts & Disciplines
ISBN : UCR:31210007102849

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N-Widths in Approximation Theory by A. Pinkus Pdf

My original introduction to this subject was through conservations, and ultimate ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction . . . . . . . . Chapter II. Basic Properties of n-Widths . 9 1. Properties of d • • • • • • • • • • 9 n 15 2. Existence of Optimal Subspaces for d • n n 17 3. Properties of d • • • • • • 20 4. Properties of b • • • • • • n 5. Inequalities Between n-Widths 22 n 6. Duality Between d and d • • 27 n 7. n-Widths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References . . . . . . . . . . . . . .

Author : S.P. Singh
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401126342

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Approximation Theory, Spline Functions and Applications by S.P. Singh Pdf

These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor tant subject. The work involves key techniques in approximation theory cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas cale, R. Charron, and B.

Author : A.A. Gonchar,E.B. Saff
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461229667

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Progress in Approximation Theory by A.A. Gonchar,E.B. Saff Pdf

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.

Author : Marek Kowalski,Christopher Sikorski,Frank Stenger
Publisher : Oxford University Press
Page : 366 pages
File Size : 51,6 Mb
Release : 1995-08-31
Category : Mathematics
ISBN : 9780195359770

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Selected Topics in Approximation and Computation by Marek Kowalski,Christopher Sikorski,Frank Stenger Pdf

Selected Topics in Approximation and Computation addresses the relationship between modern approximation theory and computational methods. The text 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 with the theory of s-numbers and n-widths. It can serve as a text for senior-graduate courses in computer science and applied mathematics, and also as a reference for professionals.

Author : E. W. Cheney
Publisher : SIAM
Page : 74 pages
File Size : 54,7 Mb
Release : 1986-10-01
Category : Mathematics
ISBN : 9780898712070

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Multivariate Approximation Theory by E. W. Cheney Pdf

This monograph deals with the development of algorithms or the derivation of approximations from linear projections.

Author : Elliott Ward Cheney,William Allan Light
Publisher : American Mathematical Soc.
Page : 379 pages
File Size : 41,9 Mb
Release : 2009-01-13
Category : Mathematics
ISBN : 9780821847985

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A Course in Approximation Theory by Elliott Ward Cheney,William Allan Light Pdf

This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

Author : C. K. Chui,Larry L. Schumaker,J. D. Ward
Publisher : Unknown
Page : 816 pages
File Size : 51,7 Mb
Release : 1983
Category : Approximation theory
ISBN : UOM:39015015733432

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Approximation Theory IV by C. K. Chui,Larry L. Schumaker,J. D. Ward Pdf

Author : Fontanella F,Jetter Kurt,Laurent P J
Publisher : World Scientific
Page : 380 pages
File Size : 51,7 Mb
Release : 1996-11-13
Category : Electronic
ISBN : 9789814547192

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Advanced Topics In Multivariate Approximation - Proceedings Of The International Workshop by Fontanella F,Jetter Kurt,Laurent P J Pdf

This volume consists of 24 refereed carefully edited papers on various topics in multivariate approximation. It represents the proceedings of a workshop organized by the University of Firenze, and held in September 1995 in Montecatini, Italy.The main themes of the volume are multiresolution analysis and wavelets, multidimensional interpolation and smoothing, and computer-aided geometric design. A number of particular topics are included, like subdivision algorithms, constrained approximation and shape-preserving algorithms, thin plate splines, radial basis functions, treatment of scattered data, rational surfaces and offsets, blossoming, grid generation, surface reconstruction, algebraic curves and surfaces, and neural networks.

Author : C. K. Chui,Larry L. Schumaker
Publisher : World Scientific
Page : 454 pages
File Size : 47,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9789814532600

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Approximation Theory Eight by C. K. Chui,Larry L. Schumaker Pdf

This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.

Author : William A. Light,Elliot W. Cheney
Publisher : Springer
Page : 164 pages
File Size : 54,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540397410

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Approximation Theory in Tensor Product Spaces by William A. Light,Elliot W. Cheney Pdf