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Mathematics of Computation

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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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Keywords: Hankel and Toeplitz matrices, triangular decomposition of matrices, fast algorithms, rational approximation
Article copyright: © Copyright 1980 American Mathematical Society

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