Some properties of biorthogonal polynomials and their application to Padé approximations
Transformations of biorthogonal polynomials under certain transformations of biorthogonalizable sequences are studied. The obtained result is used to construct Padé approximants of orders $[N−1/N],\; N \in ℕ,$ for the functions $$\tilde f(z) = \sum\limits_{m = 0}^M {\alpha _m } \frac{{f(z) - T_{m -...
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| Datum: | 1994 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5650 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511878837436416 |
|---|---|
| author | Holub, A. P. Голуб, А. П. Голуб, А. П. |
| author_facet | Holub, A. P. Голуб, А. П. Голуб, А. П. |
| author_sort | Holub, A. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:15:19Z |
| description | Transformations of biorthogonal polynomials under certain transformations of biorthogonalizable sequences are studied. The obtained result is used to construct Padé approximants of orders $[N−1/N],\; N \in ℕ,$ for the functions
$$\tilde f(z) = \sum\limits_{m = 0}^M {\alpha _m } \frac{{f(z) - T_{m - 1} [f;z]}}{{z^m }},$$
where $f(z)$ is a function with known Padé approximants of the indicated orders, $T_j [f;z]$ are Taylor polynomials of degreej for the function $f(z)$, and $α_{ m, M} = \overline {1,M}$ are constants. |
| first_indexed | 2026-03-24T03:19:54Z |
| format | Article |
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| id | umjimathkievua-article-5650 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:19:54Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/09/1a3dbeef3f3976584ca1e0f8183c2009.pdf |
| spelling | umjimathkievua-article-56502020-03-19T09:15:19Z Some properties of biorthogonal polynomials and their application to Padé approximations Некоторые свойства биортогональных полиномов и их приложения к аппроксимациям Паде Holub, A. P. Голуб, А. П. Голуб, А. П. Transformations of biorthogonal polynomials under certain transformations of biorthogonalizable sequences are studied. The obtained result is used to construct Padé approximants of orders $[N−1/N],\; N \in ℕ,$ for the functions $$\tilde f(z) = \sum\limits_{m = 0}^M {\alpha _m } \frac{{f(z) - T_{m - 1} [f;z]}}{{z^m }},$$ where $f(z)$ is a function with known Padé approximants of the indicated orders, $T_j [f;z]$ are Taylor polynomials of degreej for the function $f(z)$, and $α_{ m, M} = \overline {1,M}$ are constants. Досліджені перетворення біортогональних поліномів при деяких певних перетвореннях послідовностей, що біортогоналізуються. Одержаний результат використано при побудові апрокси-мант Паде порядків $[N−1/N],\; N \in ℕ,$ функцій вигляду $$\tilde f(z) = \sum\limits_{m = 0}^M {\alpha _m } \frac{{f(z) - T_{m - 1} [f;z]}}{{z^m }},$$ де $f(z)$ — функція, для якої апроксиманти Паде вказаних порядків відомі, $T_j [f;z]$ — многочлени Тейлора порядку j функції $f(z)$ , $α_{ m, M} = \overline {1,M}$ —деякі константи. Institute of Mathematics, NAS of Ukraine 1994-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5650 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 8 (1994); 977–984 Український математичний журнал; Том 46 № 8 (1994); 977–984 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5650/7985 https://umj.imath.kiev.ua/index.php/umj/article/view/5650/7986 Copyright (c) 1994 Holub A. P. |
| spellingShingle | Holub, A. P. Голуб, А. П. Голуб, А. П. Some properties of biorthogonal polynomials and their application to Padé approximations |
| title | Some properties of biorthogonal polynomials and their application to Padé approximations |
| title_alt | Некоторые свойства биортогональных полиномов и их приложения к аппроксимациям Паде |
| title_full | Some properties of biorthogonal polynomials and their application to Padé approximations |
| title_fullStr | Some properties of biorthogonal polynomials and their application to Padé approximations |
| title_full_unstemmed | Some properties of biorthogonal polynomials and their application to Padé approximations |
| title_short | Some properties of biorthogonal polynomials and their application to Padé approximations |
| title_sort | some properties of biorthogonal polynomials and their application to padé approximations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5650 |
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