Multidimensional Continued Fractions
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Multidimensional Continued Fractions
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Author : Fritz Schweiger
language : en
Publisher: Oxford University Press, USA
Release Date : 2000
Multidimensional Continued Fractions written by Fritz Schweiger and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Mathematician Fritz Schweiger, whose academic affiliation is not provided, provides an introduction to a field of research that has seen remarkable progress in recent decades, concentrating on multidimensional continued fractions which can be described by fractional linear maps or equivalently by a set of (n + 1) x (n + 1) matrices. Addressing the question of periodicity, he refines the problem of convergence to the question of whether these algorithms give "good" simultaneous Diophantine approximations. He notes that these algorithms are not likely to provide such "good" approximations which satisfy the n-dimensional Dirichlet property. Also studied are the ergodic properties of these maps. Annotation copyrighted by Book News Inc., Portland, OR
Geometry Of Continued Fractions
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Author : Oleg Karpenkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-15
Geometry Of Continued Fractions written by Oleg Karpenkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Mathematics categories.
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.
Continued Fractions
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Author : Doug Hensley
language : en
Publisher: World Scientific
Release Date : 2006-03-01
Continued Fractions written by Doug Hensley and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with Mathematics categories.
The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of the past decade and more, many of the results have not been brought together in book form. Continued fractions have been studied from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation.This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.
Continued Fractions
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Author : A. M. Rockett
language : en
Publisher: World Scientific
Release Date : 1992-08-01
Continued Fractions written by A. M. Rockett and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-01 with Mathematics categories.
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.
Continued Fractions
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Author : Lisa Lorentzen
language : en
Publisher: atlantis press
Release Date : 2008
Continued Fractions written by Lisa Lorentzen and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Geometry Of Continued Fractions
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Author : Oleg N. Karpenkov
language : en
Publisher: Springer Nature
Release Date : 2022-05-28
Geometry Of Continued Fractions written by Oleg N. Karpenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-28 with Mathematics categories.
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 second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. 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. 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.
Continued Fractions
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Author : Aleksandr I?Akovlevich Khinchin
language : en
Publisher: Courier Corporation
Release Date : 1997-05-14
Continued Fractions written by Aleksandr I?Akovlevich Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-14 with Mathematics categories.
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.
Continued Fractions With Applications
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Author : L. Lorentzen
language : en
Publisher: North Holland
Release Date : 1992-11-08
Continued Fractions With Applications written by L. Lorentzen and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-08 with Computers categories.
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.
Continued Fractions And Orthogonal Functions
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Author : S. Clement Cooper
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Continued Fractions And Orthogonal Functions written by S. Clement Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
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.
Continued Fractions
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Author :
language : en
Publisher:
Release Date : 1961
Continued Fractions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.