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Continued Fractions with Applications

1992-11-08 Computers
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Release : 1992-11-08
Genre : Computers
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Continued Fractions with Applications by : L. Lorentzen

Download or read book Continued Fractions with Applications written by L. Lorentzen. This book was released on 1992-11-08. Available in PDF, EPUB and Kindle. Book excerpt: 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

2008-04-01 Mathematics
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Release : 2008-04-01
Genre : Mathematics
Kind : eBook
Book Rating : 376/5 ( reviews)

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Book Synopsis CONTINUED FRACTIONS by : Haakon Waadeland

Download or read book CONTINUED FRACTIONS written by Haakon Waadeland. This book was released on 2008-04-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continued Fractions

1997-05-14 Mathematics
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Release : 1997-05-14
Genre : Mathematics
Kind : eBook
Book Rating : 300/5 ( reviews)

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Book Synopsis Continued Fractions by : Aleksandr I?Akovlevich Khinchin

Download or read book Continued Fractions written by Aleksandr I?Akovlevich Khinchin. This book was released on 1997-05-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Continued Fractions

2013-08-15 Mathematics
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Release : 2013-08-15
Genre : Mathematics
Kind : eBook
Book Rating : 683/5 ( reviews)

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Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg Karpenkov. This book was released on 2013-08-15. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Signal Processing

2021-09-06 Mathematics
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Release : 2021-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 602/5 ( reviews)

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Book Synopsis Continued Fractions and Signal Processing by : Tomas Sauer

Download or read book Continued Fractions and Signal Processing written by Tomas Sauer. This book was released on 2021-09-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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