Influence of poles on equioscillation in rational approximation
The error curve for rational best approximation of f ∈ 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 to be dense in...
Збережено в:
| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164020 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Influence of poles on equioscillation in rational approximation / H.-P. Blatt // Український математичний журнал. — 2006. — Т. 58, № 1. — С. 3–11. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The error curve for rational best approximation of f ∈ 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 to be dense in [−1, 1]. The reason is the influence
of the distribution of the poles of the 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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