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Volume 2, Issue 2
Existence of Rational Interpolation Function and an Open Problems of P. Turán

Guo-Liang Xu

J. Comp. Math., 2 (1984), pp. 170-179.

Published online: 1984-02

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  • Abstract

An existence theorem of rational interpolation function for the sufficient condition has correctly been stated by Macon-Dupree in [2], but some arguments in their proof are not true. In this paper: (i) A related theorem for both the sufficient and necessary condition is asserted and proved by a new and rigorous approach, namely by introducing the notion of (m/n) quasi-rational interpolant of a given function. (ii) With use of these results thus obtained an open problem proposed by P. Turán in [4] is completely solved.

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@Article{JCM-2-170, author = {Guo-Liang Xu}, title = {Existence of Rational Interpolation Function and an Open Problems of P. Turán}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {2}, pages = {170--179}, abstract = {

An existence theorem of rational interpolation function for the sufficient condition has correctly been stated by Macon-Dupree in [2], but some arguments in their proof are not true. In this paper: (i) A related theorem for both the sufficient and necessary condition is asserted and proved by a new and rigorous approach, namely by introducing the notion of (m/n) quasi-rational interpolant of a given function. (ii) With use of these results thus obtained an open problem proposed by P. Turán in [4] is completely solved.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9651.html} }
TY - JOUR T1 - Existence of Rational Interpolation Function and an Open Problems of P. Turán AU - Guo-Liang Xu JO - Journal of Computational Mathematics VL - 2 SP - 170 EP - 179 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9651.html KW - AB -

An existence theorem of rational interpolation function for the sufficient condition has correctly been stated by Macon-Dupree in [2], but some arguments in their proof are not true. In this paper: (i) A related theorem for both the sufficient and necessary condition is asserted and proved by a new and rigorous approach, namely by introducing the notion of (m/n) quasi-rational interpolant of a given function. (ii) With use of these results thus obtained an open problem proposed by P. Turán in [4] is completely solved.

Guo-Liang Xu. (1984). Existence of Rational Interpolation Function and an Open Problems of P. Turán. Journal of Computational Mathematics. 2 (2). 170-179. doi:
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