Optimal Polynomial Meshes Exist on any Multivariate Convex Domain
نویسندگان
چکیده
We show that optimal polynomial meshes exist for every convex body in $${\mathbb {R}}^d$$ , confirming a conjecture by A. Kroó.
منابع مشابه
On optimal polynomial meshes
Let P d n be the the space of real algebraic polynomials of d variables and degree at most n, K ⊂ R a compact set, ||p||K := supx∈K |p(x)| the usual supremum norm on K, card(Y ) the cardinality of a finite set Y . A family of sets Y = {Yn ⊂ K, n ∈ N} is called an admissible mesh in K if there exists a constant c1 > 0 depending only on K such that ||p||K ≤ c1||p||Yn , p ∈ P d n , n ∈ N, where th...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2023
ISSN: ['1615-3383', '1615-3375']
DOI: https://doi.org/10.1007/s10208-023-09606-x