Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries

P. -A. Absil, Luca Amodei, Gilles Meyer

We consider two Riemannian geometries for the manifold $\mathcal{M}(p,m\times n)$ of all $m\times n$ matrices of rank $p$. The geometries are induced on $\mathcal{M}(p,m\times n)$…