Matrix interpretation of multiple orthogonality

Branquinho, A.; Cotrim, L.; Moreno, A. Foulquié

http://hdl.handle.net/10400.8/14735

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Matrix interpretation of multiple orthogonality.pdf	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-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.	223.48 KB	Adobe PDF	Download

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Authors

Branquinho, A.

Cotrim, L.

Moreno, A. Foulquié

Abstract(s)

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-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.

Description

Fonte: https://www.researchgate.net/publication/220393901_Matrix_interpretation_of_multiple_orthogonality

Keywords

Multiple-orthogonal polynomials Hermite-Pad´e approximants block tridiagonal operator Favard type theorem

URI

http://hdl.handle.net/10400.8/14735

Citation

Branquinho, 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.