Comparison of approximation properties of generalized polynomials and splines
We establish that, for p ∈ [2, ∞), q = 1 or p = ∞, q ∈ [ 1, 2], the classes W p r of functions of many variables defined by restrictions on the L p-norms of mixed derivatives of order r = (r 1, r 2, ..., r m) are better approximated in the L q-metric by periodic generalized splines than by generali...
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| Date: | 1998 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4850 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish that, for p ∈ [2, ∞), q = 1 or p = ∞, q ∈ [ 1, 2], the classes W p r of functions of many variables defined by restrictions on the L p-norms of mixed derivatives of order r = (r 1, r 2, ..., r m) are better approximated in the L q-metric by periodic generalized splines than by generalized trigonometric polynomials. In these cases, the best approximations of the Sobolev classes of functions of one variable by trigonometric polynomials and by periodic splines coincide. |
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