Pade Approximation and Its Applications
Author : L. Wuytack
Publisher :
Page : 404 pages
File Size : 23,25 MB
Release : 2014-09-01
Category :
ISBN : 9783662199978
Author : L. Wuytack
Publisher :
Page : 404 pages
File Size : 23,25 MB
Release : 2014-09-01
Category :
ISBN : 9783662199978
Author : L. Wuytack
Publisher : Springer
Page : 403 pages
File Size : 44,36 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540385118
Author : Amilcare Pozzi
Publisher : World Scientific
Page : 257 pages
File Size : 50,96 MB
Release : 1994-03-07
Category : Mathematics
ISBN : 9814504092
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.
Author : M.G. de Bruin
Publisher : Springer
Page : 393 pages
File Size : 26,10 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540386068
Author : A. Bultheel
Publisher : Birkhäuser
Page : 277 pages
File Size : 48,43 MB
Release : 2012-12-06
Category : Science
ISBN : 303489306X
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 : 24,83 MB
Release : 1975-01-01
Category : Science
ISBN : 0323156150
Essentials of Padé Approximants
Author : Jean Bourgain
Publisher :
Page : 306 pages
File Size : 38,98 MB
Release : 1981
Category : Lp spaces
ISBN : 9780387111544
Author : H. Werner
Publisher : Springer
Page : 273 pages
File Size : 32,57 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540389148
Author : George Allen Baker
Publisher : Cambridge University Press
Page : 762 pages
File Size : 32,77 MB
Release : 1996-01-26
Category : Mathematics
ISBN : 0521450071
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 :
Publisher : Academic Press
Page : 398 pages
File Size : 25,68 MB
Release : 1971-02-27
Category : Mathematics
ISBN : 0080955800
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