Interpolation of data by smooth non-negative functions
arXiv:1603.0233050 citationsh-index: 62
Originality Incremental advance
AI Analysis
For mathematicians and researchers in approximation theory, this result offers a rigorous framework for nonnegative interpolation, though it is a theoretical advance without immediate practical applications.
The paper proves a finiteness principle for interpolation of data by nonnegative C^m functions, establishing that the existence of such an interpolant can be determined by checking a finite number of points. This provides a theoretical foundation for constrained interpolation problems.
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.