Matrix interpretation of multiple orthogonality

Abstract: In 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-ortogonality 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-Pad´e approximation in matrix form is given.

• Type: Journal
• Year: 2010
• Where: NA
• Authors: Amílcar Branquinho, Luis Cotrim, Ana Foulquié Moreno
• Keywords: Matrix, NA 2010, Recurrence Relation, Type Ii