Title

Fast Bellman algorithm for real Monge-Ampere equation

Abstract

In this talk I will introduce a new numerical algorithm solving the Dirichlet problem for real Monge-Ampere equation. The algorithm is based on Bellman's principle which enables to solve our fully non-linear elliptic Monge-Ampere equation by approximating it with a sequence of linear elliptic differential equations. Further, I will discuss the strengths and weaknesses of the method whilst demonstrating its performance on many examples of various degrees of degeneracy as well as compare its efficiency with two other numerical methods, which emerges to be 3-10 times faster for smooth, convex examples and 20-100 times faster for mildly degenerate examples.