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Discrete Aleksandrov solutions of the Monge-Ampere equation (1408.1729v4)
Published 7 Aug 2014 in math.NA and cs.NA
Abstract: We prove the convergence of a wide stencil finite difference scheme to the Aleksandrov solution of the elliptic Monge-Ampere equation when the right hand side is a sum of Dirac masses. The discrete scheme we analyze for the Dirichlet problem, when coupled with a discretization of the second boundary condition, can be used to get a good initial guess for geometric methods solving optimal transport between two measures.