Row Convergence Theorems for Vector-Valued Padé Approximants

Graves‐Morris, P. R.; Iseghem, Jeannette Van

doi:10.1006/jath.1996.3077

Cited by 9 publications

(2 citation statements)

References 27 publications

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“…We also present consequences for the numerator polynomial. The presence of only polar singularities on the boundary |z|=|z o+1 |, allows the derivation of stronger results than those published hitherto [10,20].…”

Section: Introductionmentioning

confidence: 92%

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A Vector Generalisation of de Montessus' Theorem for the Case of Polar Singularities on the Boundary

Roberts

2002

Journal of Approximation Theory

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In the context of vector Padé approximants we present an extension of de Montessus' theorem to vector-valued meromorphic functions with poles on the boundary of interest-thus strengthening previous results for these approximants. The proofs are framed in Clifford algebras which provide a natural language for discussing vector rational approximants. We also present results for the asymptotic behaviour of the constituent parts of the Clifford denominator-namely, its scalar and bivector parts. In particular, for the case of vector-valued rational functions in which the principal parts are orthogonal to each other for different poles, we demonstrate that the rate of convergence is doubled for the scalar part of the denominator. Finally, we derive consequences of the convergence theorems for the approximation of poles, using either the complete Clifford denominator or its scalar part.

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Section: Introductionmentioning

confidence: 92%

“…However, there is more than one extension of Padé approximation to vector-valued functions cf. [10,28]-in particular we refer to the work of Sidi. Here we investigate those approximants derived using the vector inverse of v :…”

Section: Introductionmentioning

confidence: 99%