有理関数による補間に対する重心形式の数式処理における利用について

Abstract

Barycentric-type formulae for rational function interpolations are studied from the view-point of computer algebra. In order to determine the interpolation by a rational function of a given degree, we avoid solving the system of equations for the numerator and denominator coefficients of the rational function representing the conditions at the set of interpolation points. Instead, we use a barycentric-type form to represent in advance the rational functions that satisfy the conditions at the set of interpolation points. As an example of the use of this method, we present the design of the transfer-function of a filters to approximate those eigenpairs of a generalized eigenproblem whose eigenvalues are lower-exterior.