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An efficient numerical method for the solution of the \(L_2\) optimal mass transfer problem. (English) Zbl 1428.49034

Summary: In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal \(L_2\) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent et al., SIAM J. Math. Anal. 35, No. 1, 61–97 (2003; Zbl 1042.49040)], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.

MSC:

49M37 Numerical methods based on nonlinear programming
90C20 Quadratic programming

Citations:

Zbl 1042.49040
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