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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 4, Pages 822–832 (Mi smj1006)  
This article is cited in 2 scientific papers (total in 2 papers)

Convergence conditions for interpolation fractions at the nodes distinct from the singular points of a function

A. G. Lipchinskii

Ishim State Pedagogical Institute
Full-text PDF (193 kB) Citations (2)
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Abstract: We consider an interpolation process for the class of functions with finitely many singular points by means of the rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes constitute a triangular matrix and are distinct from the singular points of the function. We find a necessary and sufficient condition for uniform convergence of sequences of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence.
Keywords: function, singular point of a function, interpolation process, rational fraction, uniform convergence, divergence.
Received: 19.10.2004
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 4, Pages 652–660
DOI: https://doi.org/10.1007/s11202-005-0065-3
Bibliographic databases:
UDC: 517.53
Language: Russian
Citation: A. G. Lipchinskii, “Convergence conditions for interpolation fractions at the nodes distinct from the singular points of a function”, Sibirsk. Mat. Zh., 46:4 (2005), 822–832; Siberian Math. J., 46:4 (2005), 652–660
Citation in format AMSBIB
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\pages 822--832
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\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 4
\pages 652--660
\crossref{https://doi.org/10.1007/s11202-005-0065-3}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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