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Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold
We show that on the manifold of fixed-rank and symmetric positive semi-definite matrices, the Riemannian gradient descent algorithm almost surely escapes some spurious critical points on the boundary of the manifold.
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization
The first one is a rank-1 matrix recovery problem.
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition
In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework.
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