TY - JOUR
T1 - On the Solvability of Rational Hermite-Interpolation Problem
AU - Guo-Liang Xu & Jia-Kai Li
JO - Journal of Computational Mathematics
VL - 3
SP - 238
EP - 251
PY - 1985
DA - 1985/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9621.html
KW - 
AB - <p style="text-align: justify;">The solvability of the rational Hermite-interpolation problem is investigated through an approach similar to that developed in an earlier paper [1] for the ordinary case. However, the subsequent deduction of analogous results involves much complications. The Quasi-Rational Hermite Interpolant $r_{mn}^{*}$ is introduced. In the case of $r_{mn}^{*}$ being nondegenerate, its explicit expression is given. Working with the notion of l-fold unattainable point and using algebraic elaboration, we have successively established several theorems concerning interpolating properties of $r_{mn}^{*}$ and, in particular, obtained existence theorems for the solution of the proposed problem. &nbsp;</p>