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 plan...

In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...