Pade Approximation and its Applications
Author: L. Wuytack
Publisher: Springer
Published: 2006-11-15
Total Pages: 403
ISBN-13: 3540385118
DOWNLOAD EBOOK →Author: L. Wuytack
Publisher: Springer
Published: 2006-11-15
Total Pages: 403
ISBN-13: 3540385118
DOWNLOAD EBOOK →Author: A. Bultheel
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 277
ISBN-13: 303489306X
DOWNLOAD EBOOK →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: Amilcare Pozzi
Publisher: World Scientific
Published: 1994-03-07
Total Pages: 257
ISBN-13: 9814504092
DOWNLOAD EBOOK →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: Amilcare Pozzi
Publisher: World Scientific
Published: 1994
Total Pages: 257
ISBN-13: 9810214146
DOWNLOAD EBOOK →Although Pad presented his fundamental paper at the end of the last century, the studies on Pad's approximants only became significant in the second part of this century.Pad procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Pad 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 Pad approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Pad 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 Pad 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 Pad 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 Pad approximants to unsteady flows.
Author: M.G. de Bruin
Publisher: Springer
Published: 2006-12-08
Total Pages: 393
ISBN-13: 3540386068
DOWNLOAD EBOOK →Author: H. Werner
Publisher: Springer
Published: 2006-12-08
Total Pages: 273
ISBN-13: 3540389148
DOWNLOAD EBOOK →Author: George A. Jr. Baker
Publisher: Elsevier
Published: 1975-01-01
Total Pages: 319
ISBN-13: 0323156150
DOWNLOAD EBOOK →Essentials of Padé Approximants
Author: Conference on Padé Approximation and Its Applications
Publisher:
Published: 1972
Total Pages:
ISBN-13:
DOWNLOAD EBOOK →Author: H. Werner
Publisher:
Published: 2014-01-15
Total Pages: 276
ISBN-13: 9783662174333
DOWNLOAD EBOOK →