Guo-Liang Xu ¹, Jia-Kai Li ¹

The solvability of the rational Hermite-interpolation problem is investigated through an approach similar to that developed in an earlier papor[1] for the ordinary case. However, the subsequent deduction of analogous results involves much complications. The Qusi-Rational Hermite Interpolant $r_{mn}^{*}$ is introduced. In the case of $r_{mn}^{*}$ being nondegenerate, its explicit expression is given. Working with the motion of l-fold unattainablepoint and using algebraic elaboration, we have successively established several theorems concerning interpolating properties of $r_{mn}^{*}$ and , in particular, obatained existence theorems for the solution of the proposed problem.

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