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

摘要

A kind of function-valued Pade-type approximant via the formal orthogonal polynomials (FPTAVOP) is introduced oil 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. (C) 2007 Elsevier B.V. All rights reserved.