Continued Fractions And Signal Processing PDF Download
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| Author | : Tomas Sauer |
| Publisher | : Springer Nature |
| Total Pages | : 275 |
| Release | : 2021-09-06 |
| Genre | : Mathematics |
| ISBN | : 3030843602 |
Download Continued Fractions and Signal Processing Book in PDF, ePub and Kindle
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 | : Claude Brezinski |
| Publisher | : North Holland |
| Total Pages | : 354 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
Download Continued Fractions and Padé Approximants Book in PDF, ePub and Kindle
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 | : S. Clement Cooper |
| Publisher | : CRC Press |
| Total Pages | : 402 |
| Release | : 2020-12-17 |
| Genre | : Mathematics |
| ISBN | : 1000154149 |
Download Continued Fractions and Orthogonal Functions Book in PDF, ePub and Kindle
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 | : Lisa Lorentzen |
| Publisher | : atlantis press |
| Total Pages | : 321 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9078677074 |
Download Continued Fractions Book in PDF, ePub and Kindle
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 | : Claude Brezinski |
| Publisher | : |
| Total Pages | : 354 |
| Release | : 1991 |
| Genre | : Continued fractions |
| ISBN | : |
Download A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects Book in PDF, ePub and Kindle
| Author | : L. Lorentzen |
| Publisher | : North Holland |
| Total Pages | : 634 |
| Release | : 1992-11-08 |
| Genre | : Computers |
| ISBN | : |
Download Continued Fractions with Applications Book in PDF, ePub and Kindle
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 | : Hubert Stanley Wall |
| Publisher | : Courier Dover Publications |
| Total Pages | : 449 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486830446 |
Download Analytic Theory of Continued Fractions Book in PDF, ePub and Kindle
One of the most authoritative and comprehensive books on the subject of continued fractions, this monograph has been widely used by generations of mathematicians and their students. Dr. Hubert Stanley Wall presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. Prerequisites include a first course in function theory and knowledge of the elementary properties of linear transformations in the complex plane. Some background in number theory, real analysis, and complex analysis may also prove helpful. The two-part treatment begins with an exploration of convergence theory, addressing continued fractions as products of linear fractional transformations, convergence theorems, and the theory of positive definite continued fractions, as well as other topics. The second part, focusing on function theory, covers the theory of equations, matrix theory of continued fractions, bounded analytic functions, and many additional subjects.
| Author | : Aleksandr I?Akovlevich Khinchin |
| Publisher | : Courier Corporation |
| Total Pages | : 116 |
| Release | : 1997-05-14 |
| Genre | : Mathematics |
| ISBN | : 9780486696300 |
Download Continued Fractions Book in PDF, ePub and Kindle
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 | : Andrew M Rockett |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 200 |
| Release | : 1992-08-08 |
| Genre | : Mathematics |
| ISBN | : 9813103418 |
Download Continued Fractions Book in PDF, ePub and Kindle
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 | : Annie A.M. Cuyt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 430 |
| Release | : 2008-04-12 |
| Genre | : Mathematics |
| ISBN | : 1402069499 |
Download Handbook of Continued Fractions for Special Functions Book in PDF, ePub and Kindle
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!
