Computational Methods and Function Theory 10 (2010), No. 1, 223--247
Copyright Heldermann Verlag 2010
Avram Sidi
asidi@cs.technion.ac.il , Technion — Israel Institute of Technology, Computer Science Department, Haifa 32000, Israel.
We continue our study of convergence of IMPE, one of the vector-valued rational interpolation procedures proposed by the author in a recent paper, in the context of vector-valued meromorphic functions with simple poles. So far, this study has been carried out in the presence of corresponding residues that are mutually orthogonal. In the present work, we continue to study IMPE in the same context, but in the presence of corresponding residues that are not necessarily orthogonal. Choosing the interpolation points appropriately, we derive de Montessus type convergence results for the interpolants and König type results for the poles and residues.
Keywords: Vector-valued rational interpolation, Hermite interpolation, Newton interpolation formula, de Montessus Theorem, König Theorem.
MSC 2000: Primary 30E10, 41A05, 41A20, 41A25, 41A60; Secondary 65D05.
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