Interpolation Of Functions

Author : J Szabados,P Vértesi
Publisher : World Scientific
Page : 320 pages
File Size : 48,7 Mb
Release : 1990-10-16
Category : Electronic
ISBN : 9789814507370

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Interpolation of Functions by J Szabados,P Vértesi Pdf

This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics. Contents:Lagrange InterpolationSome Convergent Interpolatory ProcessesThe Lebesgue Function and Lebesgue Function-Type SumsDivergence of Lagrange InterpolationHermite-Fejér and Hermite-Fejér Type InterpolationsComparison of Lagrange and Hermite-Fejér InterpolationsSome Problems in the Theory of Lacunary InterpolationMiscellaneous ProblemsSome Frequently Used Relation and Theorems Readership: Mathematicians. Keywords:Lagrange Interpolation;Divergence of the Interpolation;Lebesgue Function;Lebesgue Constant;Hermite-Fejer Interpolation;Convergent Interpolatory ProcessesReview:“… this is a very careful and exhaustive treatment of interpolation by univariate polynomials … It is the proverbial book nobody in the area can do without.”J Approximation Theory “… this is the first monograph devoted entirely to interpolation … As a whole this book can serve as an excellent and valuable deskcopy for researchers as well as for graduate students in approximation theory and related fields.”Acta Sci. Math. (Szeged)

Author : Kristian Seip
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 45,6 Mb
Release : 2004
Category : Analytic functions
ISBN : 9780821835548

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Interpolation and Sampling in Spaces of Analytic Functions by Kristian Seip Pdf

Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an

Author : Joseph Ball,I. Gohberg,Rodman
Publisher : Birkhäuser
Page : 605 pages
File Size : 53,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034877091

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Interpolation of Rational Matrix Functions by Joseph Ball,I. Gohberg,Rodman Pdf

This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).

Author : Jim Agler,John E. McCarthy
Publisher : American Mathematical Society
Page : 330 pages
File Size : 44,9 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470468552

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Pick Interpolation and Hilbert Function Spaces by Jim Agler,John E. McCarthy Pdf

The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Author : Giuseppe Mastroianni,Gradimir Milovanovic
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 40,9 Mb
Release : 2008-08-24
Category : Mathematics
ISBN : 9783540683490

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Interpolation Processes by Giuseppe Mastroianni,Gradimir Milovanovic Pdf

Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (orthogonal polynomials, moduli of smoothness,K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.

Author : J. L. Walsh
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 54,6 Mb
Release : 1935-12-31
Category : Mathematics
ISBN : 9780821810200

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Interpolation and Approximation by Rational Functions in the Complex Domain by J. L. Walsh Pdf

The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Author : Tom Christiansen,Nathan Torkington
Publisher : "O'Reilly Media, Inc."
Page : 967 pages
File Size : 45,5 Mb
Release : 2003-08-21
Category : Computers
ISBN : 9780596554965

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Perl Cookbook by Tom Christiansen,Nathan Torkington Pdf

Find a Perl programmer, and you'll find a copy of Perl Cookbook nearby. Perl Cookbook is a comprehensive collection of problems, solutions, and practical examples for anyone programming in Perl. The book contains hundreds of rigorously reviewed Perl "recipes" and thousands of examples ranging from brief one-liners to complete applications.The second edition of Perl Cookbook has been fully updated for Perl 5.8, with extensive changes for Unicode support, I/O layers, mod_perl, and new technologies that have emerged since the previous edition of the book. Recipes have been updated to include the latest modules. New recipes have been added to every chapter of the book, and some chapters have almost doubled in size.Covered topic areas include: Manipulating strings, numbers, dates, arrays, and hashes Pattern matching and text substitutions References, data structures, objects, and classes Signals and exceptions Screen addressing, menus, and graphical applications Managing other processes Writing secure scripts Client-server programming Internet applications programming with mail, news, ftp, and telnet CGI and mod_perl programming Web programming Since its first release in 1998, Perl Cookbook has earned its place in the libraries of serious Perl users of all levels of expertise by providing practical answers, code examples, and mini-tutorials addressing the challenges that programmers face. Now the second edition of this bestselling book is ready to earn its place among the ranks of favorite Perl books as well.Whether you're a novice or veteran Perl programmer, you'll find Perl Cookbook, 2nd Edition to be one of the most useful books on Perl available. Its comfortable discussion style and accurate attention to detail cover just about any topic you'd want to know about. You can get by without having this book in your library, but once you've tried a few of the recipes, you won't want to.

Author : Alessandra Lunardi
Publisher : Springer
Page : 199 pages
File Size : 50,8 Mb
Release : 2018-05-05
Category : Mathematics
ISBN : 9788876426384

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Interpolation Theory by Alessandra Lunardi Pdf

This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.

Author : Philip J. Davis
Publisher : Courier Corporation
Page : 418 pages
File Size : 49,8 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 9780486624952

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Interpolation and Approximation by Philip J. Davis Pdf

Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.

Author : I. J. Schoenberg
Publisher : SIAM
Page : 127 pages
File Size : 50,5 Mb
Release : 1973-01-01
Category : Mathematics
ISBN : 9780898710090

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Cardinal Spline Interpolation by I. J. Schoenberg Pdf

In this book the author explains cardinal spline functions, the basic properties of B-splines and exponential Euler splines.

Author : Borislav D. Bojanov,H. Hakopian,B. Sahakian
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 44,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401581691

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Spline Functions and Multivariate Interpolations by Borislav D. Bojanov,H. Hakopian,B. Sahakian Pdf

Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Author : Joseph Leonard Walsh
Publisher : Unknown
Page : 426 pages
File Size : 40,5 Mb
Release : 1965
Category : Functions
ISBN : STANFORD:36105030749001

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Interpolation and Approximation by Rational Functions in the Complex Domain by Joseph Leonard Walsh Pdf

Author : I. Gohberg
Publisher : Birkhäuser
Page : 257 pages
File Size : 44,7 Mb
Release : 2013-11-21
Category : Science
ISBN : 9783034854696

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Topics in Interpolation Theory of Rational Matrix-valued Functions by I. Gohberg Pdf

One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.

Author : Borislav D. Bojanov,H. Hakopian,B. Sahakian
Publisher : Springer
Page : 278 pages
File Size : 53,8 Mb
Release : 2014-03-14
Category : Mathematics
ISBN : 9401581703

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Spline Functions and Multivariate Interpolations by Borislav D. Bojanov,H. Hakopian,B. Sahakian Pdf

Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Author : I. Gohberg
Publisher : Birkhäuser
Page : 305 pages
File Size : 44,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034877015

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Extension and Interpolation of Linear Operators and Matrix Functions by I. Gohberg Pdf