Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry

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 nonexpansive fixed point iterations new tool called the scaled relative graph (SRG). The SRG provides correspondence between nonlinear operators subsets 2D plane. Under framework, argument plane becomes rigorous proof convergence.