By a discrete version of Tchakaloff Theorem on positive quadrature formulas, we prove that any real multidimensional compact set admitting a Markov polynomial inequality with exponent 2 possesses a near optimal polynomial mesh. This improves for example previous results on general convex bodies and starlike bodies with Lipschitz boundary, being applicable to any compact set satisfying a uniform interior cone condition. We also discuss two algorithmic approaches for the computation of near optimal Tchakaloff meshes in low dimension.
Near optimal Tchakaloff meshes for compact sets with Markov exponent 2
Vianello M. (2018) "Near optimal Tchakaloff meshes for compact sets with Markov exponent 2 " Dolomites Research Notes on Approximation, 11(4), 79-83. DOI: 10.14658/PUPJ-DRNA-2018-4-8
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Dolomites Research Notes on Approximation
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