Research output: Contribution to journal › Article › peer-review
We treat the interpolation problem { f (x j ) = y j } Nj=1 for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences of special symmetric functions of the data set like {∑ Nj=1 xkj y j /W ′ (x j )} k ∈N and {∑ Nj=1 xkj /(y j W ′ (x j ))} k ∈N; here, W(x) = ∏ Nj=1 (x − x j ). We also review the results by Jacobi, Joachimsthal, Kronecker and Frobenius on the recursive procedure for computation of the sequence of Hankel polynomials. The problem of evaluation of the resultant of polynomials p(x) and q(x) given a set of values {p(x j )/q(x j )} Nj=1 is also tackled within the framework of this approach. An effective procedure is suggested for recomputation of rational interpolants in case of extension of the data set by an extra point.
Translated title of the contribution | Рациональная интерполяция: реминисценция метода Якоби. |
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Original language | English |
Article number | 1401 |
Number of pages | 35 |
Journal | Symmetry |
Volume | 13 |
Issue number | 8 |
DOIs | |
State | Published - 1 Aug 2021 |
ID: 84400875