NUDELMAN INTERPOLATION AND THE BAND METHOD

In previous work the authors developed a new addition of the band meth od based on a Grassmannian approach for solving a completion/extension problem in a general, abstract framework. This addition allows one to obtain a linear fractional representation of all solutions of the abs tract completion problem from special extensions which are not necessa rily band extensions (for the positive case) or triangular extensions (for the contractive case). In this work we extend this framework to a somewhat more general setting and show how one can obtain formulas fo r the required special extensions from solutions of a system of linear equations. As an application we show how the formalism can be applied to the bitangential Nevanlinna-Pick interpolation problem, a case whi ch, up to now, was not amenable to the band method.