Novel alternating update method for low rank approximation of structured matrices

作者：Bai, Jianchao^*; Li, Jicheng^*; Dai, Pingfan

来源：Applied Numerical Mathematics, 2017, 121: 223-233.

DOI：10.1016/j.apnum.2017.07.001

• Alternating update method
• Low rank approximation
• Structured matrix
• System identification

This work is devoted to designing a unified alternating update method for solving a class of structured low rank approximations under the convex and unitarily invariant norm. By the aid of the variational inequality and monotone operator, the proposed method is proved to converge to the solution point of an equivalent variational inequality with a worst case O(1/t) convergence rate in a nonergodic sense. We also analyze that the involved subproblems under the Frobenius norm are respectively equivalent to the structured least squares problem and low rank least-squares problem, where the explicit solutions to some special cases are derived. In order to investigate the efficiency of the proposed method, several examples in system identification are tested to validate that the proposed method can outperform some state-of-the-art methods.

• 出版日期2017-11
• 单位三明学院; 西安交通大学