In this paper we obtain an algorithm for the truncated matrix Hausdorff moment problem with an odd number of given moments. The coefficients of the corresponding linear fractional matrix transformation can be calculated using the prescribed moments. No conditions besides solvability are assumed for the moment problem. The question of the determinateness of the moment problem is answered by (a part of) the algorithm as well. Several examples are provided.
"An Algorithm for the Truncated Matrix Hausdorff Moment Problem." Commun. Math. Anal. 17 (2) 108 - 130, 2014.