Interpolation operators on the space of holomorphic functions on the unit circle. (Q1771823)
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scientific article; zbMATH DE number 2158705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Interpolation operators on the space of holomorphic functions on the unit circle. |
scientific article; zbMATH DE number 2158705 |
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Interpolation operators on the space of holomorphic functions on the unit circle. (English)
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19 April 2005
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In the first part of the paper, the author constructs the error-estimate of the remainder of a general interpolation formula. The usual assumptions concerning the higher derivatives of the interpolated function are replaced here by the assumption that the interpolated function has a holomorphic extension on a circle in the complex plane containing the (real) interval of its definition. The estimate obtained then does not depend on the derivatives of the interpolated function. The second part of the paper is devoted to the construction of optimal interpolation formulae via minimization in the above manner of constructed estimates.
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numerical interpolation
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optimal interpolatory rule with prescribed nodes
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optimal interpolatory rule with free nodes
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remainder estimation
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