How to compute the polar factorization of a matrix in a way you shouldn't

Abstract: The polar factorization is a way to decompose a square matrix into the product of an orthogonal factor and a positive-definite symmetric factor. There exist various ways to do this fast and efficiently, but in this talk, I would like to present a method that is neither fast nor efficient. In fact, it is completely inadvisable and should not be used for any application relying in any way on computing the polar factorization. It is, however, interesting for an entirely different reason, in that it arises in an unexpected and fascinating way. After having showcased the method, I will briefly explain its derivation by discussing the Gaussian optimal transport problem, principal fiber bundles, and gradient flows to showcase that even numerical linear algebra can have deep geometric roots.

Mathematics

Audience: general audience

Gothenburg PhD seminar

Series comments: Rooms and times may vary, please check the latest update. In-person only.