Abstract
This paper is concerned with double sequencesC={C n} =−∞/∞n of Hermitian matrices with complex entriesC n ∈M s×s ) and formal Laurent seriesL 0(z)=−Σ ∞ k=1 C −k z k andL ∞(z)=Σ ∞ k=0 C k z −k. Making use of a Favard-type theorem for certain sequences of matrix Laurent polynomials which was obtained previously in [1] we can establish the relation between the matrix counterpart of the so-calledT-fractions and matrix orthogonal Laurent polynomials. The connection with two-point Padé approximants to the pair (L 0,L ∞) is also exhibited proving that such approximants are Hermitian too. Finally, error formulas are also given.
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González-Concepción, C., González-Vera, P. & Hendriksen, E. Matrix orthogonal Laurent polynomials and two-point Padé approximants. Numer Algor 3, 201–209 (1992). https://doi.org/10.1007/BF02141929
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DOI: https://doi.org/10.1007/BF02141929