Interpolation of Set-Valued Functions

TL;DR

This paper develops efficient methods for approximating continuous set-valued functions from finite samples, enabling practical computation of such functions in applications involving compact subsets of the real line.

Contribution

It introduces novel approximation techniques for set-valued functions based on finite samples, improving computational efficiency and accuracy.

Findings

New approximation algorithms for set-valued functions

Efficient computation methods demonstrated

Improved accuracy over existing approaches

Abstract

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.