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Birkhoff interpolation on unity and on Möbius transform of the roots of unity

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Abstract

In this paper the regularity of two interpolation problems is proved. One uses (0,1,..., r-2,r) interpolation with as nodes Möbius transforms of nth roots of unity with the point z=1 added and the other is concerned with Pál-type interpolation on the pair of polynomials (z+α)n+(1+α z)n and (z+α)n-(1+α z)n, where 0 < α < 1.

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Authors and Affiliations

  1. Department of Applied Mathematical Analysis, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    M.G. de Bruin

  2. R.D. University, Jabalpur, India, 482001

    H.P. Dikshit

  3. M.P. Bhoj (Open) University, Bhopal, India, 462016

    H.P. Dikshit

  4. Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

    A. Sharma

Authors
  1. M.G. de Bruin
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  2. H.P. Dikshit
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  3. A. Sharma
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de Bruin, M., Dikshit, H. & Sharma, A. Birkhoff interpolation on unity and on Möbius transform of the roots of unity. Numerical Algorithms 23, 115–125 (2000). https://doi.org/10.1023/A:1019147900265

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  • DOI: https://doi.org/10.1023/A:1019147900265

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