Bi-orthogonality in rational approximation

摘要

The well-known connection between Padé approximants to Stieltjes functions and orthogonal polynomials is crucial in locating zeros and poles and in convergence theorems. In the present paper we extend similar types of analysis to more elaborate forms of approximation. It transpires that the link with orthogonal polynomials remains valid with regard to rational interpolants, whereas simultaneous Padé and Levin—Sidi approximants yield themselves to analysis with bi-orthogonal polynomials.