A Numerical Model for the Construction of Finite Blaschke Products with Preassigned Distinct Critical Points

We present a numerical model for determining a finite Blaschke product of degree n+1nhaving  nnpreassigned distinct critical points z1,...,znin the complex (open) unit disk D. The Blaschke product is uniquely determined up to postcomposition with conformal automorphisms of D. The proposed method is based on the construction of a sparse nonlinear system where the data dependency is isolated to two vectors and on a certain transformation of the critical points. The efficiency and accuracy of the method is illustrated in several examples.