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A de Montessus Type Convergence Study of a Least-Squares Vector-Valued Rational Interpolation Procedure II

机译:最小二乘向量值有理插值程序的de Montessus型收敛性研究II

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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 Konig type results for the poles and residues.
机译:在具有简单极点的向量值亚纯函数的背景下,我们将继续研究IMPE的收敛性,IMPE是作者最近在论文中提出的向量值有理插值方法之一。到目前为止,这项研究是在存在相互正交的相应残基的情况下进行的。在目前的工作中,我们将在相同的背景下继续研究IMPE,但是在存在不一定正交的相应残基的情况下。适当选择插值点,我们得出插值的de Montessus型收敛结果,以及极点和残差的Konig型结果。

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