Continued Fractions And Padé Approximants

Author : Claude Brezinski
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581694

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History of Continued Fractions and Padé Approximants by Claude Brezinski Pdf

The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...

Author : Claude Brezinski
Publisher : North Holland
Page : 354 pages
File Size : 41,8 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015024806385

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Continued Fractions and Padé Approximants by Claude Brezinski Pdf

Padeacute; approximants and continued fractions are typical examples of old areas of mathematics (continued fractions can be traced back to Euclid's g.c.d. algorithm more than 2000 years ago) which are again very much alive. This is due to their numerous applications in number theory, cryptography, statistics, numerical analysis, special functions, digital filtering, signal processing, fractals, fluid mechanics, theoretical physics, chemistry, engineering etc. This renewal of interest is also due to their intimate connection with other important topics such as orthogonal polynomials (another old subject now again in full vitality), rational approximation, Gaussian quadratures, extrapolation and convergence acceleration methods, differential equations etc.

Author : Claude Brezinski
Publisher : Springer Verlag
Page : 551 pages
File Size : 49,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0387152865

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History of Continued Fractions and Padé Approximants by Claude Brezinski Pdf

The concept of continued fractions os one of the oldest in the history of mathematics. It can be traced back to Euclid's algorithm for the greatest common divisor or even earlier. Continued fractions and Pade approximants played an important role in the development of many branches of mathematics, such as the spectral theory of operators, and in the solution of famous problems, such as the quadrature of the circle.

Author : Claude Brezinski
Publisher : Unknown
Page : 354 pages
File Size : 42,5 Mb
Release : 1991
Category : Continued fractions
ISBN : UOM:39015050447716

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A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects by Claude Brezinski Pdf

Author : L. Lorentzen,H. Waadeland
Publisher : North Holland
Page : 636 pages
File Size : 47,5 Mb
Release : 1992-11-08
Category : Computers
ISBN : UOM:39076001255129

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Continued Fractions with Applications by L. Lorentzen,H. Waadeland Pdf

This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.

Author : Lisa Lorentzen,Haakon Waadeland
Publisher : atlantis press
Page : 321 pages
File Size : 46,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9789078677079

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Continued Fractions by Lisa Lorentzen,Haakon Waadeland Pdf

Continued Fractions consists of two volumes -- Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given.This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.

Author : Carl Douglas Olds
Publisher : Mathematical Association of America (MAA)
Page : 186 pages
File Size : 46,6 Mb
Release : 1963
Category : Mathematics
ISBN : PSU:000027139950

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Continued Fractions by Carl Douglas Olds Pdf

Author : Hubert Stanley Wall
Publisher : Courier Dover Publications
Page : 449 pages
File Size : 41,6 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486823690

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Analytic Theory of Continued Fractions by Hubert Stanley Wall Pdf

One of the most authoritative and comprehensive books on continued fractions, this monograph presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. 1948 edition.

Author : E. B. Saff,Richard S. Varga
Publisher : Unknown
Page : 510 pages
File Size : 50,7 Mb
Release : 1977
Category : Mathematics
ISBN : MINN:319510005371409

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Padé and Rational Approximation by E. B. Saff,Richard S. Varga Pdf

Author : Annie A.M. Cuyt,Vigdis Petersen,Brigitte Verdonk,Haakon Waadeland,William B. Jones
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 40,8 Mb
Release : 2008-04-12
Category : Mathematics
ISBN : 9781402069499

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Handbook of Continued Fractions for Special Functions by Annie A.M. Cuyt,Vigdis Petersen,Brigitte Verdonk,Haakon Waadeland,William B. Jones Pdf

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

Author : Leo Jerome Lange,Bruce C. Berndt,Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 41,6 Mb
Release : 1999-07-28
Category : Mathematics
ISBN : 0821855727

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Continued Fractions by Leo Jerome Lange,Bruce C. Berndt,Fritz Gesztesy Pdf

This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields--from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Pade approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Author : Bruce C. Berndt,Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 49,5 Mb
Release : 1999
Category : Continued fractions
ISBN : 9780821812006

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Continued Fractions: From Analytic Number Theory to Constructive Approximation by Bruce C. Berndt,Fritz Gesztesy Pdf

This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Author : George Allen Baker,Peter Graves-Morris
Publisher : Cambridge University Press
Page : 762 pages
File Size : 44,8 Mb
Release : 1996-01-26
Category : Mathematics
ISBN : 9780521450072

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Pade Approximants by George Allen Baker,Peter Graves-Morris Pdf

The first edition of this book was reviewed in 1982 as "the most extensive treatment of Pade approximants actually available." This second edition has been thoroughly updated, with a substantial new chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

Author : A. M. Rockett,Peter Szsz
Publisher : World Scientific
Page : 202 pages
File Size : 48,7 Mb
Release : 1992-08-01
Category : Mathematics
ISBN : 9810210523

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Continued Fractions by A. M. Rockett,Peter Szsz Pdf

This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.

Author : E.B. Safe
Publisher : Elsevier
Page : 506 pages
File Size : 53,6 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9780323147774

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Pade and Rational Approximation by E.B. Safe Pdf

Padé and Rational Approximation: Theory and Applications presents the proceedings of the Conference on Rational Approximation with Emphasis on Applications of Padé Approximants, held in Tampa, Florida on December 15-17, 1976. The contributors focus on the interplay of theory, computation, and physical applications. This book is composed of six parts encompassing 44 chapters. The introductory part discusses the general theory of orthogonal polynomials that is the mathematical basis of Padé approximants and related matters evaluation. This text also examines the connection between approximants on a stepline in the ordinary Padé table and certain continued fractions and the convergence of diagonal Padé approximants to a class of functions with an even number of branch points. The following parts deal with the special functions and continued fractions of Padé approximation and the theory of rational approximations. These parts also investigate the geometric convergence of Chebyshev rational approximation on the half line, the optimal approximation by “Almost Classical interpolation, and the incomplete polynomials approximation. The discussion then shifts to the physical applications and computations of the Padé approximants. The concluding part presents the applications of rational approximation to gun fire control and to the White Sands Missile Range Computer Facility. This part also provides a list of some open problems and conjectures concerning polynomials and rational functions. This book is of great benefit to mathematicians, physicists, and laboratory workers.