Lower estimates on the saturation order of approximation of twice continuously differentiable functions by piecewise constants on convex partitions

O.V. Kozynenko

doi:10.15421/241805

Lower estimates on the saturation order of approximation of twice continuously differentiable functions by piecewise constants on convex partitions

O.V. Kozynenko (Oles Honchar Dnipro National University)

Abstract

We consider the problem of approximation order of twice continuously differentiable functions of many variables by piecewise constants. We show that the saturation order of piecewise constant approximation in $$$L_p$$$ norm on convex partitions with $$$N$$$ cells is $$$N^{-2/(d+1)}$$$, where $$$d$$$ is the number of variables.

Keywords

twice continuously differentiable functions; piecewise constant splines; saturation order; convex partitions

MSC 2020

41A40; 41A25; 46E35

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References

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