A matrix Euclidean algorithm induced by state space realization Original Research Article

This paper is concerned with the study of several types of matrix interpolation problems, including • • The matrix Nevanlinna-Pick interpolation problem in the Nevanlinna class image,• • The matrix Nevanlinna-Pick interpolation problem in the Stieltjes class image,• • The truncated matrix power moment problem on the real axis,• • The Stieltjes matrix power moment problem. We use the so-called block Hankel vector approach for the treatment of these problems and make explicit the correspondence between solutions to the Nevanlinna-Pick interpolation problem and solutions to an associated power moment problem with the block Hankel vector under consideration. This enables one not only to find existence criteria for the solutions of the Nevanlinna-Pick interpolation problem, but also to describe the solutions based on the results of power moment problem, and vice versa.