On continuous partial singular value decomposition algorithms

Low-rank matrix approximation arises in various applications. It is an effective tool in alleviating the memory and computational burdens in many algorithmic development and implementation. In this paper, two methods for computing low rank approximation are proposed and derived by utilizing optimization techniques of unconstrained merit functions. The proposed techniques led to computing low-rank matrix approximation by solving nonlinear matrix differential equations. Numerical experiments illustrate the theoretical results.