Optimal recovery of three times differentiable functions on a convex polytope inscribed in a sphere
The author proves the optimality on the class of three times differentiable functions of a certain quasi-interpolating recovery method among all non-adaptive global recovery methods. This is an extension to the optimality for the case of a \(d\)-dimensional simplex, proved for an analogous class of twice differentiable functions. Here, the recovery error is measured in the uniform norm on a \(d\)-dimensional convex polytype inscribed in a sphere and containing its circumcenter.
scientific article; zbMATH DE number 6909906
scientific article