Abstract
We show that optimal polynomial meshes exist for every convex body in \({\mathbb {R}}^d\), confirming a conjecture by A. Kroó.
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Notes
There appears to be no consistency in the literature for the names of the maximal volume-inscribed ellipsoid and the minimal volume-circumscribed ellipsoid; either one may be referred to as John’s or Löwner-John’s or Löwner’s ellipsoid. According to Busemann, Löwner discovered the uniqueness of the minimal volume ellipsoid, but this was never published. John established a characterization for these ellipsoids which implied uniqueness and other properties. An interested reader is referred to the survey [10].
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The authors thank the referees for the valuable comments and suggestions.
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Communicated by Pencho Petrushev.
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The first author was supported by NSERC of Canada Discovery grant RGPIN-2020-03909, and the second author was supported by NSERC of Canada Discovery grant RGPIN-2020-05357.
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Dai, F., Prymak, A. Optimal Polynomial Meshes Exist on any Multivariate Convex Domain. Found Comput Math (2023). https://doi.org/10.1007/s10208-023-09606-x
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DOI: https://doi.org/10.1007/s10208-023-09606-x