Step-by-step solving of ordered interpolational problem for Stieltjes functions

In this paper we investigate a step-by-step solving of ordered generalized interpolation problems for the Stieltjes matrix functions and obtain a multiplicative representation of the sequence of resolvent matrices. The matrix factors in multiplicative representation of resolvent matrices are expressed through the Schur–Stieltjes parameters, for which we obtain explicit formulas, and adduce an algorithm of step-by-step solving of Stieltjes type interpolation problems. As examples, we consider step-by-step solving of Stieltjes matrix moment problem, Nevanlinna–Pick problem and Caratheodory problem.