Abstract: Starting from the Netflix problem of movie rating matrix completion in 2006, many computational algorithms have been proposed to complete a matrix. Several theories have been developed to show possible low rank matrix completion and recovery. I shall first survey several numerical algorithms: the singular value thresholding method (SVT), a fixed point method, an SOR algorithm, a linearized augmented Lagrange method, alternative direction method, an lp nonconvex minimization method, and etc. Then I will explain two excellent algorithms for matrix completion/recovery. One is called orthogonal rank-one matrix pursuit (OR1MP) algorithm and one is called alternating projection (AP) algorithm. Convergence of these two algorithms will be explained. In particular, the linear convergence of these two algorithms will be outlined. Finally I shall show some numerical results and a comparison with other algorithms will be given.
Biography: Ming-Jun Lai is an currently a Professor of Mathematics at the University of Georgia. His area of research is splines and their numerical analysis. Lai received a B.Sc. from Hangzhou University and a Ph.D. in mathematics from the Texas A&M University in 1989.
Last Updated: May 28, 2020 - 4:06 pm