Approximating geodesics via random points

Erik Davis, Sunder Sethuraman

Given a `cost' functional $F$ on paths $\gamma$ in a domain $D\subset {\mathbb{R}}^d$, in the form $F(\gamma )={\int }_0^{1}f(\gamma (t),\dot{\gamma }(t))dt$, it is of interest to approximate its minimum cost a…