The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, drawback of the known approaches is that rank parameter has to fixed priori. In this paper, we consider set bounded-rank matrices. We propose rank-adaptive method, which consists optimization, increase step and reduction step. explore its performance applied problem. Numerical expe...

A rank-adaptive integrator for the dynamical low-rank approximation of matrix and tensor differential equations is presented. The fixed-rank recently proposed by two authors extended to allow an adaptive choice rank, using subspaces that are generated itself. first updates evolving bases then does a Galerkin step in subspace both new old bases, which followed rank truncation given tolerance. It...