Wen, ZaiwenYin, WotaoZhang, Yin2018-06-192018-06-192010-03Wen, Zaiwen, Yin, Wotao and Zhang, Yin. "Solving a Low-Rank Factorization Model for Matrix Completion by a Non-linear Successive Over-Relaxation Algorithm." (2010) <a href="https://hdl.handle.net/1911/102150">https://hdl.handle.net/1911/102150</a>.https://hdl.handle.net/1911/102150The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value decompositions -- a task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale problems, we propose a low-rank factorization model and construct a nonlinear successive over-relaxation (SOR) algorithm that only requires solving a linear least squares problem per iteration. Convergence of this nonlinear SOR algorithm is analyzed. Numerical results show that the algorithm can reliably solve a wide range of problems at a speed at least several times faster than nuclear-norm minimization algorithms.24 ppengTechnical reportTR10-07