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Author : L. Wuytack
Publisher : Springer
Page : 403 pages
File Size : 42,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385110
Author : E. B. Saff,Richard S. Varga
Publisher : Unknown
Page : 510 pages
File Size : 42,6 Mb
Release : 1977
Category : Mathematics
ISBN : MINN:319510005371409
Author : George Allen Baker,Peter Graves-Morris
Publisher : Cambridge University Press
Page : 762 pages
File Size : 40,5 Mb
Release : 1996-01-26
Category : Mathematics
ISBN : 9780521450072
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
Page : 148 pages
File Size : 46,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540388784
Author : George Allen Baker
Publisher : Unknown
Page : 328 pages
File Size : 50,8 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:39015001323107
Author : Claude Brezinski
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581694
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 : E.B. Safe
Publisher : Elsevier
Page : 506 pages
File Size : 55,8 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9780323147774
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 : A Pozzi
Publisher : World Scientific
Page : 252 pages
File Size : 52,9 Mb
Release : 1994-03-07
Category : Mathematics
ISBN : 9789814504096
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. Contents:Part 1: Padé Approximants:Elements of Padé Approximants TheorySome Theoretical Aspects of Padé ApproximantsPart 2: The Fluid-Dynamic Equations:Balance EquationsInner-Outer ExpansionsPart 3: Some Examples of Application of Padé Approximants in Steady Flows:The Thermo-Fluid-Dynamic EquationsFlows Over Bodies in Forced Convection: The Flat Plate CaseForced Convection in Stagnation FlowAppendix: Motion Equations in the Odograph PlaneFlows Over Bodies in Forced Convection: The Wedge CaseThe Coupling of Conduction with Laminar Natural Convection Along a Vertical Flat PlateVariable-Properties Effects: Supersonic Wedge FlowVariable-Properties Effects: Free ConvectionPlane Jet into a Moving MediumPart 4: Some Examples of Application of Padé Approximants in Unsteady Flows:The Impulsively Started Flow Away From a Plane Stagnation PointThe Impulsively Started Flow Past a Circular Cylinder Readership: Applied mathematicians (fluid mechanics) and aerospace engineers. keywords:Pade' Approximants;Expansions in Series;Approximate Methods in Fluid-Mechanics;Boundary Layers Approximations
Author : M.G. de Bruin,H. van Rossum
Publisher : Springer
Page : 393 pages
File Size : 41,7 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540386063
Author : A. Bultheel
Publisher : Birkhäuser
Page : 277 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034893060
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 Allen Baker,P. R. Graves-Morris
Publisher : Unknown
Page : 244 pages
File Size : 45,8 Mb
Release : 1981
Category : Science
ISBN : MINN:319510005371433
Author : P. R. Graves-Morris
Publisher : Unknown
Page : 376 pages
File Size : 42,7 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015003715656
Author : Anonim
Publisher : Academic Press
Page : 398 pages
File Size : 44,7 Mb
Release : 1971-02-27
Category : Mathematics
ISBN : 9780080955803
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Author : A. Cuyt
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400929012
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 : Annie Cuyt
Publisher : Springer
Page : 160 pages
File Size : 48,5 Mb
Release : 1984
Category : Mathematics
ISBN : UCSD:31822000129189