The Research And Application Of Matrix Completion Problem

Matrix completion problem is widely used in control, computer version(face recognition and so on),internet survey and other areas, in recent years,the algorithms and theories about the problem are obtained rapid development. On the internet recommendation system it has also a lot of applications, such as collaborative filtering, etc, including the famous Netflix problem. This master’s thesis studies its application in sparse problem,and we adopt systematic study and research, and find some new algorithms and further improve the existing theory,and make applications in sparse problems such as compressive sensing.This thesis has some innovation points below:Firstly, A modified linearized Bregman iteration algorithm and A novel A-, A+linearized residual iteration algorithm are proposed.Secondly, the relationship between the proximal operator and the soft threshold operater is deduced, and Also we resolve the basic pursuit problems by the Moreau envelope approach.Thirdly,we use overrelaxation techniques to abtain the low-rank matrix fitting algorithm solving matrix completion problem.At last, we propose a new derivation method of alternating iterative algorithm and use this algorithm for solving the nonnegative matrix decomposition problem.