Pade Approximants
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History Of Continued Fractions And Pad Approximants
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Author : Claude Brezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
History Of Continued Fractions And Pad Approximants written by Claude Brezinski 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 2012-12-06 with Mathematics categories.
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 ...
Pade Approximants For Operators
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Author : A. Cuyt
language : en
Publisher: Springer
Release Date : 2006-12-08
Pade Approximants For Operators written by A. Cuyt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Pade Approximants
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Author : George Allen Baker
language : en
Publisher: Cambridge University Press
Release Date : 1996-01-26
Pade Approximants written by George Allen Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-26 with Mathematics categories.
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.
Pade Approximation And Its Applications
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Author : L. Wuytack
language : en
Publisher: Springer
Release Date : 2006-11-15
Pade Approximation And Its Applications written by L. Wuytack and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Pade Approximants
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Author : George Allen Baker
language : en
Publisher: Cambridge University Press
Release Date : 1996-01-26
Pade Approximants written by George Allen Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-26 with Mathematics categories.
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.
Pade And Rational Approximation
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Author : E.B. Safe
language : en
Publisher: Elsevier
Release Date : 2013-05-09
Pade And Rational Approximation written by E.B. Safe and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 with Mathematics categories.
Padé and Rational Approximation: Theory and Applications presents the proceedings of the Conference on Rational Approximation with Emphasis on Applications of Padé Approximants, held in Tampa, Florida on December 15-17, 1976. The contributors focus on the interplay of theory, computation, and physical applications. This book is composed of six parts encompassing 44 chapters. The introductory part discusses the general theory of orthogonal polynomials that is the mathematical basis of Padé approximants and related matters evaluation. This text also examines the connection between approximants on a stepline in the ordinary Padé table and certain continued fractions and the convergence of diagonal Padé approximants to a class of functions with an even number of branch points. The following parts deal with the special functions and continued fractions of Padé approximation and the theory of rational approximations. These parts also investigate the geometric convergence of Chebyshev rational approximation on the half line, the optimal approximation by "Almost Classical interpolation, and the incomplete polynomials approximation. The discussion then shifts to the physical applications and computations of the Padé approximants. The concluding part presents the applications of rational approximation to gun fire control and to the White Sands Missile Range Computer Facility. This part also provides a list of some open problems and conjectures concerning polynomials and rational functions. This book is of great benefit to mathematicians, physicists, and laboratory workers.
Pade Approximation And Its Applications Amsterdam 1980
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Author : M.G. de Bruin
language : en
Publisher: Springer
Release Date : 2006-12-08
Pade Approximation And Its Applications Amsterdam 1980 written by M.G. de Bruin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Applications Of Pade Approximation Theory In Fluid Dynamics
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Author : Amilcare Pozzi
language : en
Publisher: World Scientific
Release Date : 1994-03-07
Applications Of Pade Approximation Theory In Fluid Dynamics written by Amilcare Pozzi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-07 with Mathematics categories.
Although Padé presented his fundamental paper at the end of the last century, the studies on Padé's approximants only became significant in the second part of this century.Padé procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Padé approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Padé approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Padé approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Padé approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Padé approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Padé approximants to unsteady flows.
Pade Approximants And Their Applications
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Author : P. R. Graves-Morris
language : en
Publisher:
Release Date : 1973
Pade Approximants And Their Applications written by P. R. Graves-Morris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
Nonlinear Numerical Methods And Rational Approximation
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Author : A. Cuyt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Numerical Methods And Rational Approximation written by A. Cuyt 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 2012-12-06 with Mathematics categories.
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; use Stein spaces. And in addition to this there are and prediction and electrical engineering can such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.