A nondegenerate interpolation continued fraction
UDC 517.518:519.652 We prove that the Thiele's interpolation continued fraction has either \(2k-1\) approximants when the function is a polynomial of the \(k\)th degree or \(2k\) approximants for the function \(g(z) =a/(z-\alpha)^k.\) We specify the conditions under which the coeffici...
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| Дата: | 2026 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8698 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.518:519.652
We prove that the Thiele's interpolation continued fraction has either \(2k-1\) approximants when the function is a polynomial of the \(k\)th degree or \(2k\) approximants for the function \(g(z) =a/(z-\alpha)^k.\) We specify the conditions under which the coefficients of the continued fraction are finite and different from zero. For a given set of values of the functions at the nodes, we propose an algorithm that either constructs a nondegenerate interpolation continued fraction or establishes the impossibility of this construction. We also present some examples. |
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| DOI: | 10.3842/umzh.v77i5.8698 |