Abstract
This paper studies some cases of (0,m)-interpolation on non-uniformly distributed roots of unity that were not covered before. The interpolation problem uses as nodes the zeros of (z k+1)(z 3−1) with k=3n+1, 3n+2. Proof of the regularity is more intricate than when k is divisible by 3, the case included in a previous paper by the authors. The interpolation problem appears to be regular for m≤k+3, a result that is in tune with the case k=3n mentioned before. However, it is necessary to treat the full general 18×18 linear system. For small values of m the determinant is calculated explicitly using MAPLE V, Release 5.
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References
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de Bruin, M.G., Sharma, A. Birkhoff interpolation on non-uniformly distributed roots of unity. Numerical Algorithms 25, 123–138 (2000). https://doi.org/10.1023/A:1016652822276
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DOI: https://doi.org/10.1023/A:1016652822276