Theoretical Foundations for Pseudo-Inversion of Nonlinear Operators

Eyal Gofer, Guy Gilboa

Abstract: The Moore-Penrose inverse is widely used in physics, statistics, and various fields of engineering. It captures well the notion of inversion of linear operators in the case of overcomplete data. In data science, nonlinear operators are extensively used. In this paper we characterize the fundamental properties of a pseudo-inverse (PI) for nonlinear operators.