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math.OC2023★ 6 cited
Wasserstein Gradient Flows of the Discrepancy with Distance Kernel on the Line
Johannes Hertrich, Robert Beinert, Manuel Gräf +1
This paper provides results on Wasserstein gradient flows between measures on the real line. Utilizing the isometric embedding of the Wasserstein space in…
math.OC2022★ 10 cited
Wasserstein Steepest Descent Flows of Discrepancies with Riesz Kernels
Johannes Hertrich, Manuel Gräf, Robert Beinert +1
The aim of this paper is twofold. Based on the geometric Wasserstein tangent space, we first introduce Wasserstein steepest descent flows. These are locally absolutely continuous c…
math.OC2019
Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization
Martin Ehler, Manuel Gräf, Sebastian Neumayer +1
The approximation of probability measures on compact metric spaces and in particular on Riemannian manifoldsby atomic or empirical ones is a classical task in approximation and com…