An extension of the Grünwald-Marcinkiewicz interpolation theorem (Q2721597)
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scientific article; zbMATH DE number 1616268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extension of the Grünwald-Marcinkiewicz interpolation theorem |
scientific article; zbMATH DE number 1616268 |
Statements
27 June 2002
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Lagrange interpolation polynomials
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Chebyshev nodes of the first kind
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divergence phenomenon
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Hermite-Fejér interpolation polynomials
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An extension of the Grünwald-Marcinkiewicz interpolation theorem (English)
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Just over 60 years ago G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite-Fejér interpolation polynomials of which Lagrange interpolation polynomials form one spesial case.
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