Paper detail

On a Simultaneous Approach to the Even and Odd Truncated Matricial Stieltjes Moment Problem I: An $α$-Schur-Stieltjes-type algorithm for sequences of complex matrices

The characterization of the solvability of matrix versions of truncated Stieltjes-type moment problems led to the class of $α$-Stieltjes non-negative definite sequences of complex $q \times q$ matrices. In [21], a parametrization of this class was introduced, the so-called $α$-Stieltjes parametrization. The main topic of this first part of the paper is the construction of a Schur-type algorithm which produces exactly the $α$-Stieltjes parametrization.