Behaviour Preserving Extensions of Univariate and Bivariate Functions

David Levin

paper

Behaviour Preserving Extensions of Univariate and Bivariate Functions

arXiv:2410.09423

Abstract

Given function values on a domain $D_{0}$ , possibly with noise, we examine the possibility of extending the function to a larger domain $D$ , $D_{0} \subset D$ . In addition to smoothness at the boundary of $D_{0}$ , the extension on $D ∖ D_{0}$ should also inherit behavioral trends of the function on $D_{0}$ , such as growth and decay or even oscillations. The approach chosen here is based upon the framework of linear models, univariate or bivariate, with constant or varying coefficients.

22 pages, 19 figures A revised version of the published paper: Levin, David. "Behavior preserving extension of univariate and bivariate functions." Advances in Quantum Chemistry. Vol. 68. Academic Press, 2014. 19-42