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pade-type approximation method for two dimensional Fredholm integral equations of the second kind

APPLIED MATHEMATICS AND COMPUTATION 2014年 246卷 71-78页

作者： Tao, Youtian Wang, Dongyin Chaohu Coll Dept Math Chaohu 238000 Peoples R China Univ Sci & Technol China Sch Math Sci Hefei 230026 Peoples R China Anhui Fuhuang Steel Struct Chaohu 238076 Peoples R China

Two dimensional Fredholm integral equation of the second kind (2DF-II) on a bounded domain D is regarded as the problem with characteristic values. A two dimensional function-valued pade-type approximation(2DFPTA) is defined. Its error formulas and convergence theorems are presented. To obtain higher order 2DFPTA, a determinantal expression and its recursive algorithm are given. In the end three numerical examples are tested, where one on the unit triangle of vertices (0, 0), (0, 1), (1, 0) and the other two on the square. The testing results show that 2DFPTA method is more accurate. (C) 2014 Elsevier Inc. All rights reserved.

关键词： pade-type approximation Fredholm integral equation Recursive algorithm

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Composed pade-type approximation

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2001年第1-2期134卷 95-112页

作者： Daras, NJ Hellen Air Force Acad Dept Math Athens Greece

We introduce pade-type (and pade) approximation to complex-valued harmonic functions in the unit disk D. This coordinate approximation is defined to be a composed pade-type approximation (respectively, a composed pade approximation). The basic properties of such an approximation are being studied and we are showing that any classical pade-type approximant to an analytic function on D coincides with a composed pade-type approximant to this function. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： pade approximation pade-type approximation composed pade-type approximation

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On the best choice for the generating polynomial of a pade-type approximation

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BIT NUMERICAL MATHEMATICS 2004年第2期44卷 245-257页

作者： Daras, NJ Hellen Air Force Acad Dept Math Dekeleia Attikis Greece

The first aim of this paper is the study and determination of the "best" choices (pointwise, L-2 and uniform) for the generating polynomial of a pade-type approximation to the Taylor series of a function analytic in an open planar disk. The second aim is to characterize the corresponding Hermite polynomial and to give some estimates for the uniform norm of a pade-type approximation error.

关键词： best L-2 approximation error of an approximation Hermite interpolation generating polynomial pade-type approximation

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The Numerical Solution for Two-dimensional Fredholm Integral Equations of Second Kind via pade-type approximation

The Numerical Solution for Two-dimensional Fredholm Integral...

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第三十二届中国控制会议

作者： Tao Youtian WANG Dongyin Department of Mathematics Chaohu College

A two-dimensional function-valued pade-type approximation(TFPTA) is difined to compute the numerical solution for two-dimensional Fredholm integral *** avoid the direct computation of TFPTA,a recursive algorithm calle... 详细信息

ISBN: (纸本)9789881563835

关键词： Fredholm Integral Equations Numerical Solution pade-type approximation

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On pade-type model order reduction of J-Hermitian linear dynamical systems

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LINEAR ALGEBRA AND ITS APPLICATIONS 2008年第10期429卷 2451-2464页

作者： Freund, Roland W. Univ Calif Davis Dept Math Davis CA 95616 USA

A simple, yet powerful approach to model order reduction of large-scale linear dynamical systems is to employ projection onto block Krylov subspaces. The transfer functions of the resulting reduced-order models of such projection methods can be characterized as pade-type approximants of the transfer function of the original large-scale system. If the original system exhibits certain symmetries, then the reduced-order models are considerably more accurate than the theory for general systems predicts. In this paper, the framework of J-Hermitian linear dynamical systems is used to establish a general result about this higher accuracy. In particular, it is shown that in the case of J-Hermitian linear dynamical systems, the reduced-order transfer functions match twice as many Taylor coefficients of the original transfer function as in the general case. An application to the SPRIM algorithm for order reduction of general RCL electrical networks is discussed. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Linear dynamical system Descriptor system Model order reduction Block Krylov subspace Projection pade-type approximation J-Hermitian Sesquilinear form SPRIM algorithm RCL network

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Convergence rate of pade-type approximants for Stieltjes functions

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1998年第1-2期99卷 47-53页

作者： Hernandez, MB Rodriguez, FC Guadalupe, JJ Lagomasino, GL Univ La Rioja Dpto Matemat & Computac Logrono Spain Univ La Laguna Dpto Analisis Matemat Tenerife Spain Univ Carlos III Madrid Dept Matemat Madrid Spain

For a nide class of Stieltjes functions we estimate the rate of convergence of pade-type approximants when the number of fixed poles represents a fixed proportion with respect to the order of the rational approximant.... 详细信息

关键词： orthogonal polynomials pade-type approximation

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pade-type approximants for generalized Euler transforms

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NUMERICAL ALGORITHMS 2014年第2期66卷 339-347页

作者： Sablonniere, P. INSA Rennes France Univ Rennes 1 IRMAR F-35042 Rennes France

We prove that sequences generated by the generalized Euler's transform can be considered as pade-type approximants obtained by Hermite interpolation of the generating function u -> (1+xu)(-1) at the endpoints of the interval [0, 1]. A first natural extension is then proposed by considering Hermite interpolation at multiple points of larger intervals.

关键词： pade-type approximation Generalized Euler transform

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Multipoint pade-type approximants. Exact rate of convergence

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CONSTRUCTIVE approximation 1998年第2期14卷 259-272页

作者： Rodriguez, FC Lagomasino, GL Univ La Habana Fac Matemat & Computac Habana 4 Cuba Univ Carlos III Madrid Dept Matemat Leganes 28911 Spain

We study the rate with which sequences of interpolating rational functions, whose poles are partially fixed, approximate Markov-type analytic functions. Applications to interpolating quadratures are given.

关键词： pade-type approximation multipoint approximation rate of convergence quadratures

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Algebraic and arithmetical properties of Mahler infinite products generated by the second degree polynomials

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RESEARCH IN NUMBER THEORY 2023年第3期9卷 1-14页

作者： Duverney, Daniel Kurosawa, Takeshi Baggio Sch Engn F-59000 Lille France Tokyo Univ Sci Dept Appl Math 1-3 KagurazakaShinjuku Tokyo 1628605 Japan

Let (a(k))(k >= 0) and (b(k))(k >= 0) be sequences of elements of a commutative field and let r >= 2 be an integer. We study the rationality of the formal Mahler infinite product Psi(0)(x) := Pi(infinity)(k=0) (1 + a(k)x(rk) + b(k)x(2rk)) by using explicit pade-type approximants. As an application, let (a(k))(k >= 0) and (b(k))(k >= 0) belong to a same number field and satisfy (as well as their denominators) certain weak growth conditions. Assume that alpha is an element of C is algebraic with 0 < vertical bar alpha vertical bar < 1. By applying Mahler's method, we obtain transcendence results for the value Psi(0)(alpha).

关键词： Transcendence Mahler function pade-type approximation

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A New pade-type Method for Computing the Matrix Exponential

A New Pade-type Method for Computing the Matrix Exponential

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The Sixth International Conference of Matrices and Operators

作者： Chun-jing Li Xiong Yuan Xiao-jing Zhu Department of Mathematics Tongji University

In this paper a new method for computing the matrix exponential is *** new approach combines the matrix pade-type approximation and the traditional scaling and squaring *** requires no inverse of matrices and therefore is more convenient for computing the matrix exponentials e with many t.A practical algorithm is presented and is verified very effective in our implementation.

关键词： matrix exponential pade-type approximation scaling and squaring backward error.

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