Choque-Rivero, A. E. Three-term recurrence relation coefficients and continued fractions related to orthogonal matrix polynomials on the finite interval \([a, b]\). (English) Zbl 1486.30011 Linear Multilinear Algebra 70, No. 4, 730-749 (2022). Summary: The four families of matrix orthogonal polynomials are considered arising in the truncated Hausdorff matrix moment (THMM) problem. Two of those families are associated with an odd number of moments and the other two with an even number of moments. The three-term recurrence relations associated with these four families are investigated. Certain explicit formulas are presented relating the three-term recurrence relation coefficients to the Dyukarev-Stieltjes parameters, the Schur complements and the orthogonal matrix polynomials associated with the THMM problem. The matrix version of the J-fraction is presented for the corresponding four extremal solutions of the THMM problem. Cited in 1 Document MSC: 30B70 Continued fractions; complex-analytic aspects Keywords:orthogonal matrix polynomials; matrix continued fractions; Schur complements; Dyukarev-Stieltjes parameters PDFBibTeX XMLCite \textit{A. E. Choque-Rivero}, Linear Multilinear Algebra 70, No. 4, 730--749 (2022; Zbl 1486.30011) Full Text: DOI References: [1] Akhiezer, NI., The classical moment problem and some related questions in analysis (1965), New York: Oliver and Boyd, New York · Zbl 0135.33803 [2] Van Assche, W.The impact of Stieltjes work on continued fractions and orthogonal polynomials. In: van Dijk G, editor. T. J. Stieltjes: collected papers. Vol. I. 1993. p. 5-37. [3] Flajolet, P., Combinatorial aspects of continued fractions, Discrete Math, 32, 125-161 (1980) · Zbl 0445.05014 [4] Viennot, X.A combinatorial interpretation of the quotient-difference algorithm. 12th International Conference on Formal Power Series and Algebraic Combinatorics. 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