Year: 2024
Type: preprint
Abstract: We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent to computing the polar factor of a square matrix. We reveal a convexity-like structure, which explains the already established tractability of the problem and show that gradient descent in the orthogonal group computes the polar factor of a square matrix with linear convergence rate if the matrix is invertible and with an algebraic one if the matrix is singular. These results are similar to the ones of Alimisis and Vandereycken (2024) for the symmetric eigenvalue problem.
Source: arXiv (Cornell University)
Authors: Alimisis, Foivos, Vandereycken, Bart
Institution: University of Geneva
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405626831