History of Continued Fractions and Padé Approximants PDF Download
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Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 3642581692
Category : Mathematics
Languages : en
Pages : 556
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Book Description
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: Springer Science & Business Media
ISBN: 3642581692
Category : Mathematics
Languages : en
Pages : 556
Get Book Here
Book Description
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
ISBN:
Category : Mathematics
Languages : en
Pages : 354
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Book Description
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: M.G. de Bruin
Publisher: Springer
ISBN: 3540386068
Category : Mathematics
Languages : en
Pages : 393
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Book Description
Author: George Allen Baker
Publisher: Cambridge University Press
ISBN: 0521450071
Category : Mathematics
Languages : en
Pages : 762
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Book Description
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: Claude Brezinski
Publisher: Springer Verlag
ISBN: 9780387152868
Category : Mathematics
Languages : en
Pages : 551
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Book Description
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: George M. Rassias
Publisher: CRC Press
ISBN: 1000943941
Category : Mathematics
Languages : en
Pages : 544
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Book Description
This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Author: Siegfried Hecker
Publisher: Springer Science & Business Media
ISBN: 9780817638566
Category : Science
Languages : en
Pages : 298
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Book Description
This collection represents a unique undertaking in scientific publishing to honor Nick Metropolis, the last survivor of the World War II Manhattan Project in Los Alamos. In this volume, some of the leading scientists and humanists of our time have contributed essays related to their respective disciplines, exploring various aspects of future developments in science and society, philosophy, national security, nuclear power, pure and applied mathematics, physics and biology, particle physics, computing, and information science.
Author:
Publisher:
ISBN:
Category : Continued fractions
Languages : en
Pages : 450
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Book Description
Author: Ivor Grattan-Guinness
Publisher: Routledge
ISBN: 1134957491
Category : Philosophy
Languages : en
Pages : 1788
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Book Description
* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 1611975948
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
