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Criterion for the appearance of singular nodes under interpolation by simple partial fractions

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Abstract

Under simple interpolation by simple partial fractions, the poles of the interpolation fraction may arise at some nodes irrespective of the values of the interpolated function at these nodes. Such nodes are said to be singular. In the presence of singular nodes, the interpolation problem is unsolvable. We establish two criteria for the appearance of singular nodes under an extension of interpolation tables and obtain an algebraic equation for calculating such nodes.

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References

  1. E. N. Kondakova, “Special Cases of Interpolation by Simple Partial Fractions,” in Abstracts of the Int. Conf. on Differential Equations and Dynamical Systems, Suzdal, 2010 (Steklov Math. Inst., Russ. Acad. Sci., Moscow, 2010), pp. 105–106.

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  4. V. I. Danchenko and E. N. Kondakova, “Chebyshev’s Alternance in the Approximation of Constants by Simple Partial Fractions,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 270, 86–96 (2010) [Proc. Steklov Inst. Math. 270, 80–90 (2010)].

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Authors and Affiliations

  1. Chair of Functional Analysis and Its Applications, Vladimir State University, ul. Gor’kogo 87, Vladimir, 600000, Russia

    V. I. Danchenko & E. N. Kondakova

Authors
  1. V. I. Danchenko
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  2. E. N. Kondakova
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Correspondence to V. I. Danchenko.

Additional information

Original Russian Text © V.I. Danchenko, E.N. Kondakova, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 278, pp. 49–58.

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Danchenko, V.I., Kondakova, E.N. Criterion for the appearance of singular nodes under interpolation by simple partial fractions. Proc. Steklov Inst. Math. 278, 41–50 (2012). https://doi.org/10.1134/S0081543812060053

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  • DOI: https://doi.org/10.1134/S0081543812060053

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