Scaled Relative Graph: Nonexpansive operators via 2D Euclidean Geometry

Understand

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 paper, 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 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 convergence.