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

We devise an efficient algorithm that, given points z1,…,zk in the open unit disk D and a set of complex numbers {fi,0,fi,1,…,fi,ni−1} assigned to each zi, 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 zi has fi,0,fi,1,…,fi,ni−1 as its first ni coefficients.