Continued Fractions With Applications

Author : L. Lorentzen,H. Waadeland
Publisher : North Holland
Page : 636 pages
File Size : 41,9 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 : A. M. Rockett,Peter Szsz
Publisher : World Scientific
Page : 202 pages
File Size : 43,7 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 : S. Clement Cooper
Publisher : CRC Press
Page : 402 pages
File Size : 45,7 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000154146

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Continued Fractions and Orthogonal Functions by S. Clement Cooper Pdf

This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials; analyses sequences of linear fractional transformations; presents convergence results, including truncation error bounds; considers discrete distributions and limit functions arising from indeterminate moment problems; discusses Szego polynomials and their applications to frequency analysis; describes the quadrature formula arising from q-starlike functions; and covers continued fractional representations for functions related to the gamma function.;This resource is intended for mathematical and numerical analysts; applied mathematicians; physicists; chemists; engineers; and upper-level undergraduate and agraduate students in these disciplines.

Author : Haakon Waadeland,Lisa Lorentzen
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 49,5 Mb
Release : 2008-04-01
Category : Mathematics
ISBN : 9789491216374

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CONTINUED FRACTIONS by Haakon Waadeland,Lisa Lorentzen 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 : Tomas Sauer
Publisher : Springer Nature
Page : 275 pages
File Size : 47,8 Mb
Release : 2021-09-06
Category : Mathematics
ISBN : 9783030843601

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Continued Fractions and Signal Processing by Tomas Sauer Pdf

Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

Author : Juan Fernández Sánchez,Jerónimo López-Salazar Codes,Juan B. Seoane Sepúlveda,Wolfgang Trutschnig
Publisher : CRC Press
Page : 154 pages
File Size : 43,8 Mb
Release : 2023-07-20
Category : Mathematics
ISBN : 9781000907582

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Generalized Notions of Continued Fractions by Juan Fernández Sánchez,Jerónimo López-Salazar Codes,Juan B. Seoane Sepúlveda,Wolfgang Trutschnig Pdf

Ancient times witnessed the origins of the theory of continued fractions. Throughout time, mathematical geniuses such as Euclid, Aryabhata, Fibonacci, Bombelli, Wallis, Huygens, or Euler have made significant contributions to the development of this famous theory, and it continues to evolve today, especially as a means of linking different areas of mathematics. This book, whose primary audience is graduate students and senior researchers, is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions. After deriving invariant ergodic measures for each of the underlying transformations on [0,1] it is shown that any of the famous formulas, going back to Khintchine and Levy, carry over to more general settings. Complementing these results, the entropy of the transformations is calculated and the natural extensions of the dynamical systems to [0,1]2 are analyzed. Features Suitable for graduate students and senior researchers Written by international senior experts in number theory Contains the basic background, including some elementary results, that the reader may need to know before hand, making it a self-contained volume

Author : Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin
Publisher : Cambridge University Press
Page : 223 pages
File Size : 42,6 Mb
Release : 2014-07-03
Category : Mathematics
ISBN : 9780521186490

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Neverending Fractions by Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin Pdf

This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

Author : Lisa Lorentzen,Haakon Waadeland
Publisher : atlantis press
Page : 321 pages
File Size : 53,7 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 : William B. Jones,Wolfgang J. Thron
Publisher : Unknown
Page : 468 pages
File Size : 45,8 Mb
Release : 1980
Category : Mathematics
ISBN : MINN:31951000495252F

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Continued Fractions by William B. Jones,Wolfgang J. Thron Pdf

Author : M. Iosifescu,Cor Kraaikamp
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 55,5 Mb
Release : 2002-09-30
Category : Mathematics
ISBN : 1402008929

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Metrical Theory of Continued Fractions by M. Iosifescu,Cor Kraaikamp Pdf

The book is essentially based on recent work of the authors. In order to unify and generalize the results obtained so far, new concepts have been introduced, e.g., an infinite order chain representation of the continued fraction expansion of irrationals, the conditional measures associated with, and the extended random variables corresponding to that representation. Also, such procedures as singularization and insertion allow to obtain most of the continued fraction expansions related to the regular continued fraction expansion. The authors present and prove with full details for the first time in book form, the most recent developments in solving the celebrated 1812 Gauss' problem which originated the metrical theory of continued fractions. At the same time, they study exhaustively the Perron-Frobenius operator, which is of basic importance in this theory, on various Banach spaces including that of functions of bounded variation on the unit interval. The book is of interest to research workers and advanced Ph.D. students in probability theory, stochastic processes and number theory.

Author : Aleksandr I?Akovlevich Khinchin,Herbert Eagle
Publisher : Courier Corporation
Page : 116 pages
File Size : 49,9 Mb
Release : 1997-05-14
Category : Mathematics
ISBN : 0486696308

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Continued Fractions by Aleksandr I?Akovlevich Khinchin,Herbert Eagle Pdf

Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.

Author : Oleg Karpenkov
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 55,7 Mb
Release : 2013-08-15
Category : Mathematics
ISBN : 9783642393686

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Geometry of Continued Fractions by Oleg Karpenkov Pdf

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Author : William Branham Jones
Publisher : Unknown
Page : 428 pages
File Size : 40,7 Mb
Release : 1984
Category : Continued fractions
ISBN : 1107087503

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Continued Fractions by William Branham Jones Pdf

This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.

Author : Carl Douglas Olds
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 44,9 Mb
Release : 1975
Category : Continued fractions
ISBN : 8210379456XXX

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Continued Fractions by Carl Douglas Olds Pdf

Author : Alekseĭ Nikolaevich Khovanskiĭ
Publisher : Unknown
Page : 232 pages
File Size : 51,6 Mb
Release : 1963
Category : Approximate computation
ISBN : UOM:39015015601373

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The Application of Continued Fractions and Their Generalizations to Problems in Approximation Theory by Alekseĭ Nikolaevich Khovanskiĭ Pdf