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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Recursive algorithms for the matrix Padé problem


Author: Adhemar Bultheel
Journal: Math. Comp. 35 (1980), 875-892
MSC: Primary 41A21; Secondary 65D15
MathSciNet review: 572862
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Abstract: A matrix triangularization interpretation is given for the recursive algorithms computing the Padé approximants along a certain path in the Padé table, which makes it possible to unify all known algorithms in this field [5], [6]. For the normal Padé table, all these results carry over to the matrix Padé problem in a straightforward way. Additional features, resulting from the noncommutativity are investigated. A generalization of the Trench-Zohar algorithm and related recursions are studied in greater detail.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0572862-4
PII: S 0025-5718(1980)0572862-4
Keywords: Hankel and Toeplitz matrices, triangular decomposition of matrices, fast algorithms, rational approximation
Article copyright: © Copyright 1980 American Mathematical Society