Recursive algorithms for the matrix Padé problem

Author:
Adhemar Bultheel

Journal:
Math. Comp. **35** (1980), 875-892

MSC:
Primary 41A21; Secondary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572862-4

MathSciNet review:
572862

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-1980-0572862-4

Keywords:
Hankel and Toeplitz matrices,
triangular decomposition of matrices,
fast algorithms,
rational approximation

Article copyright:
© Copyright 1980
American Mathematical Society