Interpolation And Approximation By Rational Functions In The Complex Domain

Author : J. L. Walsh
Publisher : American Mathematical Soc.
ISBN 13 : 0821810200
Total Pages : 418 pages
Book Rating : 4.00/5 ( download)

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Download or read book Interpolation and Approximation by Rational Functions in the Complex Domain written by J. L. Walsh and published by American Mathematical Soc.. This book was released on 1935-12-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Richard S. Varga
Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.03/5 ( download)

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Download or read book Topics in Polynomial and Rational Interpolation and Approximation written by Richard S. Varga and published by . This book was released on 1982 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Joseph Leonard Walsh
Publisher :
ISBN 13 :
Total Pages : 426 pages
Book Rating : 4.01/5 ( download)

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Download or read book Interpolation and Approximation by Rational Functions in the Complex Domain written by Joseph Leonard Walsh and published by . This book was released on 1965 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John Hamilton Curtiss
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.98/5 ( download)

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Download or read book Interpolation by Harmonic Polynomials written by John Hamilton Curtiss and published by . This book was released on 1961 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let Hn (u;z) denote the harmonic polynomial of degree at most n found by interpolation in 2n +1 points in a function u given on the boundary C of a region D of the complex z-plane. Explict formulas are derived for Hn in the case of interpolation on a circle and on an ellipse, and convergence is proved in these cases for arbitrary continuous boundary data. Various generalizations are indicated.

Author : P.R. Graves-Morris
Publisher : Springer
ISBN 13 : 3540391134
Total Pages : 541 pages
Book Rating : 4.35/5 ( download)

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Download or read book Rational Approximation and Interpolation written by P.R. Graves-Morris and published by Springer. This book was released on 2006-11-14 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : GAIER
Publisher : Springer Science & Business Media
ISBN 13 : 1461248140
Total Pages : 207 pages
Book Rating : 4.49/5 ( download)

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Download or read book Lectures on Complex Approximation written by GAIER and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications. In the last ten or fifteen years, however, the situation has changed radically. First, a great deal of significant exper~en tal data became available. Then important contributions were made to the incorporation of general relativity into the framework of quantum theory. Finally, in the last three years, exciting devel opments took place which have placed general relativity, and all the concepts behind it, at the center of our understanding of par ticle physics and quantum field theory. Firstly, this is due to the fact that general relativity is really the "original non-abe lian gauge theory," and that our description of quantum field in teractions makes extensive use of the concept of gauge invariance. Secondly, the ideas of supersymmetry have enabled theoreticians to combine gravity with other elementary particle interactions, and to construct what is perhaps the first approach to a more finite quantum theory of gravitation, which is known as super gravity.

Author : Joseph Leonard Walsh
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.93/5 ( download)

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Download or read book Approximation by Bounded Analytic Functions written by Joseph Leonard Walsh and published by . This book was released on 1957 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Carl De Boor
Publisher : American Mathematical Soc.
ISBN 13 : 9780821867433
Total Pages : 152 pages
Book Rating : 4.31/5 ( download)

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Download or read book Approximation Theory written by Carl De Boor and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : P. R. Graves-Morris
Publisher :
ISBN 13 : 9783662168851
Total Pages : 544 pages
Book Rating : 4.55/5 ( download)

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Download or read book Rational Approximation and Interpolation written by P. R. Graves-Morris and published by . This book was released on 2014-01-15 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Collatz
Publisher : Birkhäuser
ISBN 13 : 3034871864
Total Pages : 267 pages
Book Rating : 4.60/5 ( download)

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Download or read book Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6 written by Collatz and published by Birkhäuser. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Der Band enthalt Manuskripte zu Vortragen, die auf einer von den Herausgebern geleiteten Tagung tiber "Numerische Methoden der Approximationstheorie" am Mathematischen Forschungsinstitut Ober wolfach in der Zeit vom 18.-24. Januar 1981 gehalten wurden. Das Spektrum der Vortrage reichte von der klassischen Approximations theorie tiber mehrdimensionale Approximationsverfahren bis hin zu praxisbezogenen Fragestellungen. Zu den zuerst genannten Gebieten gehorten z. B. die Verfeinerung von Fehlerabschatzungen bei der Polynominterpolation, Fragen zur Eindeutigkeit, Charakterisierung optimaler Interpolationsprozesse und Algorithmen zur rationalen Interpolation. Bei den weiteren genannten Gebieten spiegel ten zahlreiche Vortrage das steigende Interesse an der mehrdimensio nalen Interpolation, insbesondere mit verschiedenen Arten von Splines wider. Hier standen u. a. Probleme der Parameterschatzung in der Medizin und Flugtechnik, Fragen der Approximationstheorie bei der Konstruktion von Plottern und stabile Algorithmen beim Arbeiten mit mehrdimensionalen B-Splines im Mittelpunkt des Interesses. Die Tagung lieferte einen reprasentativen Ueberblick tiber die aktuellen Trends in der Approximationstheorie. Zum guten Erfolg der Tagung trug wie immer die hervorragende Be treuung durch die Mitarbeiter und Angestellten des Instituts so-' wie das verstandnisvolle Entgegenkommen des Institutsdirektors, Herrn Professor Dr. Barner, bei. Un serer besonderer Dank gilt dem Birkhauser Verlag ftir die wie stets sehr gute Ausstattung. Helmut Werner Lothar Collatz Gtinther Meinardus Hamburg Mannheim Bonn 7 INDEX Blatt, H.-P. Strenge Eindeutigkeitskonstanten und Fehlerabschatzungen bei linearer Tschebyscheff-Approximation 9 Bohmer, K. Polynom- und Spline-Interpolation (Ein Farbfilm) 26 Brannigan, M.A Multivariate Adaptive Data Fitting Algorithm 30 Brass, H. Zur numerischen Berechnung konjugierter Funktionen 43 Bultheel, A