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We obtain a new multiplicative decomposition of the resolvent matrix of thetruncated Hausdorff matrix moment (THMM) problem in the case of an odd and evennumber of moments via new Dyukarev-Stieltjes matrix (DSM) parameters. Explicitinterrelations between new DSM parameters and orthogonal matrix polynomials ona finite interval $[a,b]$, as well as the Schur complements of the block Hankelmatrices constructed through the moments of the THMM problem are given.Additionally, the extremal solutions of the THMM problem are represented viamatrix continued fractions in terms of the DSM parameters.

The Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem  via New Dyukarev-Stieltjes Parameters and Extremal Solutions via Continued  Fractions