Influence of poles on equioscillation in rational approximation
The error curve for the rational best approximation of ƒ ? C[?1, 1] is characterized by the well-known equioscillation property. Contrary to the polynomial case, the distribution of these alternations is not governed by the equilibrium distribution. It is known that these points need not be dense in...
Збережено в:
| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2006
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3429 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | The error curve for the rational best approximation of ƒ ? C[?1, 1] is characterized by the well-known equioscillation property. Contrary to the polynomial case, the distribution of these alternations is not governed by the equilibrium distribution. It is known that these points need not be dense in [?1, 1]. The reason is the influence of the distribution of the poles of rational approximants. In this paper, we generalize the results known so far to situations where the requirements for the degrees of numerators and denominators are less restrictive. |
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