Corpus ID: 15655954

Solution of Interpolation Problems via the Hankel Polynomial Construction

@article{Uteshev2016SolutionOI,
  title={Solution of Interpolation Problems via the Hankel Polynomial Construction},
  author={Alexei Yu. Uteshev and Ivan Baravy},
  journal={ArXiv},
  year={2016},
  volume={abs/1603.08752}
}
We treat the interpolation problem $ \{f(x_j)=y_j\}_{j=1}^N $ for polynomial and rational functions. Developing the approach by C.Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences $ \{\sum_{j=1}^N x_j^ky_j/W^{\prime}(x_j) \}_{k\in \mathbb N} $ and $ \{\sum_{j=1}^N x_j^k/(y_jW^{\prime}(x_j)) \}_{k\in \mathbb N} $; here $ W(x)=\prod_{j=1}^N(x-x_j) $. The obtained results are applied for the error correction problem, i.e. the problem of… Expand
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