Pade And Rational Approximation

Author : E.B. Safe
Publisher : Elsevier
Page : 506 pages
File Size : 49,5 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9780323147774

Get Book

Pade and Rational Approximation by E.B. Safe Pdf

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.

Author : E. B. Saff
Publisher : Unknown
Page : 491 pages
File Size : 46,7 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:1014967005

Get Book

Padé and rational Approximation by E. B. Saff Pdf

Author : Claude Brezinski,Michela Redivo-Zaglia
Publisher : Springer Nature
Page : 410 pages
File Size : 53,7 Mb
Release : 2020-11-30
Category : Mathematics
ISBN : 9783030584184

Get Book

Extrapolation and Rational Approximation by Claude Brezinski,Michela Redivo-Zaglia Pdf

This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.

Author : E. B. Saff,Richard S. Varga
Publisher : Unknown
Page : 491 pages
File Size : 53,7 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:488765739

Get Book

Padé and Rational Approximation by E. B. Saff,Richard S. Varga Pdf

Author : L. Wuytack
Publisher : Springer
Page : 403 pages
File Size : 43,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385110

Get Book

Pade Approximation and its Applications by L. Wuytack Pdf

Author : Edward Barry Saff
Publisher : Unknown
Page : 128 pages
File Size : 51,6 Mb
Release : 1977
Category : Electronic
ISBN : 0126141509

Get Book

Padé and rational approximation : theory and applications ; [proceedings of an international symposium held at the University of South Florida, Tampa, Florida, December 15 - 17, 1976] by Edward Barry Saff Pdf

Author : Jacek Gilewicz,Maciej Pindor,Wojciech Siemaszko
Publisher : Springer
Page : 362 pages
File Size : 47,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540474128

Get Book

Rational Approximation and its Applications in Mathematics and Physics by Jacek Gilewicz,Maciej Pindor,Wojciech Siemaszko Pdf

Author : George Allen Baker,Peter Graves-Morris
Publisher : Cambridge University Press
Page : 762 pages
File Size : 43,7 Mb
Release : 1996-01-26
Category : Mathematics
ISBN : 9780521450072

Get Book

Pade Approximants by George Allen Baker,Peter Graves-Morris Pdf

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 : A. Cuyt
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 48,9 Mb
Release : 1988-01-31
Category : Mathematics
ISBN : 9027726698

Get Book

Nonlinear Numerical Methods and Rational Approximation by A. Cuyt Pdf

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.

Author : M.G. de Bruin,H. van Rossum
Publisher : Springer
Page : 393 pages
File Size : 53,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540386063

Get Book

Pade Approximation and its Applications, Amsterdam 1980 by M.G. de Bruin,H. van Rossum Pdf

Author : H. Werner,H.J. Bünger
Publisher : Springer
Page : 273 pages
File Size : 54,7 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540389149

Get Book

Pade Approximations and its Applications by H. Werner,H.J. Bünger Pdf

Author : A. Bultheel
Publisher : Birkhäuser
Page : 277 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034893060

Get Book

Laurent Series and their Padé Approximations by A. Bultheel Pdf

The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity.

Author : George A. Jr. Baker
Publisher : Elsevier
Page : 319 pages
File Size : 47,8 Mb
Release : 1975-01-01
Category : Science
ISBN : 9780323156158

Get Book

Essentials of Padé Approximants by George A. Jr. Baker Pdf

Essentials of Padé Approximants

Author : A. Cuyt
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401109703

Get Book

Nonlinear Numerical Methods and Rational Approximation II by A. Cuyt Pdf

These are the proceedings of the international conference on "Nonlinear numerical methods and Rational approximation II" organised by Annie Cuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70's. The following figures illustrate the growing number of participants and their geographical dissemination. In 1993 the Belgian scientific committee consisted of A. Bultheel (Leuven), A. Cuyt (Antwerp), J. Meinguet (Louvain-Ia-Neuve) and J.-P. Thiran (Namur). The conference focused on the use of rational functions in different fields of Numer ical Analysis. The invited speakers discussed "Orthogonal polynomials" (D. S. Lu binsky), "Rational interpolation" (M. Gutknecht), "Rational approximation" (E. B. Saff) , "Pade approximation" (A. Gonchar) and "Continued fractions" (W. B. Jones). In contributed talks multivariate and multidimensional problems, applications and implementations of each main topic were considered. To each of the five main topics a separate conference day was devoted and a separate proceedings chapter compiled accordingly. In this way the proceedings reflect the organisation of the talks at the conference. Nonlinear numerical methods and rational approximation may be a nar row field for the outside world, but it provides a vast playground for the chosen ones. It can fascinate specialists from Moscow to South-Africa, from Boulder in Colorado and from sunny Florida to Zurich in Switzerland.

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 40,7 Mb
Release : 2019-01-01
Category : Mathematics
ISBN : 9781611975949

Get Book

Approximation Theory and Approximation Practice, Extended Edition by Lloyd N. Trefethen Pdf

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 field’s 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.