Chapter 2 - Behavior Preserving Extension of Univariate and Bivariate Functions

Abstract

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 ⊂ D . In addition to smoothness at the boundary of D 0 , the extension to 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 coefficients or varying coefficients.