Near-best univariate spline discrete quasi-interpolants on non-uniform partitions
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2004
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| _version_ | 1866915560272429056 |
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| author | Barrera, D. Ibanez, M. J. Sablonniere, Paul Sbibih, D. |
| author_facet | Barrera, D. Ibanez, M. J. Sablonniere, Paul Sbibih, D. |
| contents | Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with nonuniform partitions, the main challenge is to find dQIs which have both good approximation orders and bounded uniform norms independent of the given partition. Near-best dQIs are obtained by minimizing an upper bound of the infinite norm of dQIs depending on a certain number of free parameters, thus reducing this norm. This paper is devoted to the study of some families of near-best dQIs of approximation order 2. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0405034 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Near-best univariate spline discrete quasi-interpolants on non-uniform partitions Barrera, D. Ibanez, M. J. Sablonniere, Paul Sbibih, D. Numerical Analysis 41A15; 41A35; 65D07; 65D17 Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with nonuniform partitions, the main challenge is to find dQIs which have both good approximation orders and bounded uniform norms independent of the given partition. Near-best dQIs are obtained by minimizing an upper bound of the infinite norm of dQIs depending on a certain number of free parameters, thus reducing this norm. This paper is devoted to the study of some families of near-best dQIs of approximation order 2. |
| title | Near-best univariate spline discrete quasi-interpolants on non-uniform partitions |
| topic | Numerical Analysis 41A15; 41A35; 65D07; 65D17 |
| url | https://arxiv.org/abs/math/0405034 |