  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.
