Volume 3, Issue 3
On the Solvability of Rational Hermite-Interpolation Problem
DOI:

J. Comp. Math., 3 (1985), pp. 238-251

Published online: 1985-03

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• Abstract

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.

• Keywords

@Article{JCM-3-238, author = {Guo-Liang Xu and Jia-Kai Li}, title = {On the Solvability of Rational Hermite-Interpolation Problem}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {3}, pages = {238--251}, abstract = { 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9621.html} }
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 - 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.