Function-valued Padé-type approximant via the formal orthogonal polynomials and its applications in solving integral equations

Authors:
Chuanqing Gu;Jindong Shen
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
Cited 1

Solution of integral equations using generalised inverse, function-valued Pade´ approximants, I

Journal of Computational and Applied Mathematics - Special issue on extrapolation and rational approximation
A review of Pade´ methods for the acceleration of convergence of a sequence of vectors

Selected papers of the IMACS conference on Innovative methods in numerical analysis
A family of Padé-type approximants for accelerating the convergence of sequences

Journal of Computational and Applied Mathematics
Computional Aspects of Linear Control

Computional Aspects of Linear Control
Introduction to the improved functional epsilon algorithm

Journal of Computational and Applied Mathematics

Nonlinear functional equations satisfied by orthogonal polynomials

Journal of Approximation Theory

Quantified Score

Hi-index	7.29

Visualization

Abstract

A kind of function-valued Pade-type approximant via the formal orthogonal polynomials (FPTAVOP) is introduced on the polynomial space and an algorithm is sketched by means of the formal orthogonal polynomials. This method can be applied to approximate characteristic values and the corresponding characteristic function of Fredholm integral equation of the second kind. Moreover, theoretical analyses show that FPTAVOP method is the most effective one for accelerating the convergence of a sequence of functions. In addition, a typical numerical example is presented to illustrate when the estimates of characteristic value and characteristic function by using this new method are more accurate than other methods.