Title: Scaled Relative Graph: Nonexpansive operators via 2D Euclidean Geometry

Speaker: Ernest Ryu (Seoul National University)

Date and Time: November 25th, 2020, 17:00 AEDT (Register here for remote connection via Zoom)

Abstract: Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this work, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph (SRG). The SRG provides a rigorous correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of contractiveness of the corresponding operator.