Branquinho, A.Cotrim, L.Moreno, A. Foulquié2025-11-262025-11-262009-12-18Branquinho, A., Cotrim, L. & Foulquié Moreno, A. Matrix interpretation of multiple orthogonality. Numer Algor 55, 19–37 (2010). https://doi.org/10.1007/s11075-009-9355-3.1017-1398http://hdl.handle.net/10400.8/14735Fonte: https://www.researchgate.net/publication/220393901_Matrix_interpretation_of_multiple_orthogonalityIn this work we give an interpretation of a (s (d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials. We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions. We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite-Padé approximation in matrix form is given.engMultiple-orthogonal polynomialsHermite-Pad´e approximantsblock tridiagonal operatorFavard type theoremjournal article10.1007/s11075-009-9355-31572-9265