CONVERGENCE OF THE VERTICAL GRADIENT FLOW FOR THE GAUSSIAN MONGE PROBLEM
Artikel i vetenskaplig tidskrift, 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

Författare

Erik Jansson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Journal of Computational Dynamics

2158-2505 (eISSN)

Vol. 11 1 1-9

Långtidsbeteende för tvådimensionella inkompressibla flöden via kvantisering

Vetenskapsrådet (VR) (2022-03453), 2023-01-01 -- 2026-12-31.

Ämneskategorier

Beräkningsmatematik

Reglerteknik

DOI

10.3934/jcd.2023008

Mer information

Senast uppdaterat

2024-07-02