ISSN:
1572-9265
Keywords:
AMS 15
;
41
;
Orthogonal polynomials
;
Laurent polynomials
;
T-fractions
;
Padé approximants
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02141929
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