Interpolation of data by smooth non-negative functions

TL;DR

This paper establishes a finiteness principle for interpolating data with smooth, non-negative functions, advancing understanding of constrained interpolation problems with non-negativity constraints.

Contribution

It introduces a finiteness principle for nonnegative smooth function interpolation, providing a theoretical foundation for constrained interpolation problems.

Findings

Finiteness principle for nonnegative Cm interpolation functions

Potential to understand constrained interpolation problems better

Advances theoretical understanding of non-negativity constraints in interpolation

Abstract

We prove a finiteness principle for interpolation of data by nonnegative Cm functions. Our result raises the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function F is required to be nonnegative.