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Rectangular matrix Padé approximants and square matrix orthogonal polynomials

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Abstract

In this paper we study Padé-type and Padé approximants for rectangular matrix formal power series, as well as the formal orthogonal polynomials which are a consequence of the definition of these matrix Padé approximants. Recurrence relations are given along a diagonal or two adjacent diagonals of the table of orthogonal polynomials and their adjacent ones. A matrix qd-algorithm is deduced from these relations. Recurrence relations are also proved for the associated polynomials. Finally a short presentation of right matrix Padé approximants gives a link between the degrees of orthogonal polynomials in right and left matrix Padé approximants in order to show that the latter are identical.

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Draux, A., Moalla, B. Rectangular matrix Padé approximants and square matrix orthogonal polynomials. Numerical Algorithms 14, 321–341 (1997). https://doi.org/10.1023/A:1019177316794

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