Optimal polynomial admissible meshes on some classes of compact subsets of \(\mathbb{R}^d\) (Q281559)
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scientific article; zbMATH DE number 6579069
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal polynomial admissible meshes on some classes of compact subsets of \(\mathbb{R}^d\) |
scientific article; zbMATH DE number 6579069 |
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Optimal polynomial admissible meshes on some classes of compact subsets of \(\mathbb{R}^d\) (English)
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11 May 2016
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\textit{A. Kroó} [Bull. Math. Sci. 3, No. 3, 349--361 (2013; Zbl 1284.41005)] has proved that any compact star shaped set \(K\subset\mathbb R^d\) with Minkowski functional having \(\alpha\)-Lipschitz gradient has an admissible mesh. In another paper [J. Approx. Theory 163, No. 9, 1107--1124 (2011; Zbl 1229.65049)] \textit{A. Kroó} conjectured that any real convex body has an optimal admissible mesh. In the present paper the author builds such optimal admissible meshes on two relevant classes of compact sets.
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admissible meshes
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multivariate polynomial approximation
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positive reach
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distance function
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