CONVERGENCE OF THE VERTICAL GRADIENT FLOW FOR THE GAUSSIAN MONGE PROBLEM
Journal article, 2024

We investigate a matrix dynamical system related to optimal mass transport in the linear category, namely, the problem of finding an optimal invertible matrix by which two covariance matrices are congruent. We first review the differential geometric structure of the problem in terms of a principal fiber bundle. The dynamical system is a gradient flow restricted to the fibers of the bundle. We prove global existence of solutions to the flow, with convergence to the polar decomposition of the matrix given as initial data. The convergence is illustrated in a numerical example.

Gradient flows

Matrix decompositions

Optimal transport

Author

Erik Jansson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Klas Modin

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Journal of Computational Dynamics

2158-2505 (eISSN)

Vol. 11 1 1-9

Long-time 2D hydrodynamics via quantization

Swedish Research Council (VR) (2022-03453), 2023-01-01 -- 2026-12-31.

Subject Categories

Computational Mathematics

Control Engineering

DOI

10.3934/jcd.2023008

More information

Latest update

7/2/2024 5