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

We devise an efficient algorithm that, given points z₁,…,z_k in the open unit disk D and a set of complex numbers {f_i,0,f_i,1,…,f_i,ni−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,ni−1 as its first n_i coefficients.