Nevanlinna-Pick interpolation by rational functions with a single pole inside the unit disk

We devise an efficient algorithm that, given points z 1 , ? , z k in the open unit disk D and a set of complex numbers { f i , 0 , f i , 1 , ? , f i , n i - 1 } assigned to each z i , produces a rational function f with a single (multiple) pole in D , such that f is bounded on the unit circle by a predetermined positive number, and its Taylor expansion at z i has f i , 0 , f i , 1 , ? , f i , n i - 1 as its first n i coefficients.