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Matrix interpretation of multiple orthogonality
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| 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 |
Orientador(es)
Resumo(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.
Descrição
Fonte: https://www.researchgate.net/publication/220393901_Matrix_interpretation_of_multiple_orthogonality
Palavras-chave
Multiple-orthogonal polynomials Hermite-Pad´e approximants block tridiagonal operator Favard type theorem
Contexto Educativo
Citação
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.
Editora
Springer Nature
Licença CC
Sem licença CC