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• W2774097373 abstract "We show that the discrete Sinkhorn algorithm - as applied in the setting of Optimal Transport on a compact manifold - converges to the solution of a fully non-linear parabolic PDE of Monge-Ampere type, in a large-scale limit. The latter evolution equation has previously appeared in different contexts (e.g. on the torus it can be be identified with the Ricci flow). This leads to algorithmic approximations of the potential of the Optimal Transport map, as well as the Optimal Transport distance, with explicit bounds on the arithmetic complexity of the construction and the approximation errors. As applications we obtain explicit schemes of nearly linear complexity, at each iteration, for optimal transport on the torus and the two-sphere, as well as the far-field antenna problem. Connections to Quasi-Monte Carlo methods are exploited." @default.
• W2774097373 created "2017-12-22" @default.
• W2774097373 creator A5073101289 @default.
• W2774097373 date "2017-12-08" @default.
• W2774097373 modified "2023-09-27" @default.
• W2774097373 title "The Sinkhorn algorithm, parabolic optimal transport and geometric Monge-Amp`ere equations" @default.
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• W2774097373 hasPublicationYear "2017" @default.
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