Solution of Interpolation Problems via the Hankel Polynomial Construction
Abstract
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 reconstructing the polynomial from a redundant set of its values some of which are probably erroneous. The problem of evaluation of the resultant of polynomials $ p(x) $ and $ q(x) $ from the set of values $ \{p(x_j)/q(x_j) \}_{j=1}^N $ is also tackled within the framework of this approach.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.08752
- arXiv:
- arXiv:1603.08752
- Bibcode:
- 2016arXiv160308752U
- Keywords:
-
- Computer Science - Symbolic Computation;
- 68W30;
- 30E05;
- 16D05;
- 12Y05;
- 26C15;
- I.1.2;
- G.1.1
- E-Print:
- 56 pages, 1 figure