High-Order Approximation of Set-Valued Functions

Constructive Approximation（2022）

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摘要

We introduce the notion of metric divided differences of set-valued functions. With this notion we obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions by metric piecewise-polynomial interpolants of high degree. Moreover, we derive high-order approximation of set-valued functions by local metric approximation operators reproducing high-degree polynomials.

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关键词

Set-valued functions,Metric linear combinations,Set-valued metric divided differences,Set-valued metric polynomial interpolation,Metric local linear operators,High-order approximation

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