2.2NAMay 8
On a stochastic column-block bregman method for nonlinear systemsWendi Bao, Naiyu Jiang, Lili Xing et al.
Sparse solution problems play an important role in both signal processing and image restoration. In this paper, we propose a stochastic column-block nonlinear Bregman method for efficiently computing sparse solutions to nonlinear systems. Under certain assumptions, we analyze the convergence of the proposed method and derive an upper bound for its convergence rate. Numerical experiments, including an image recovery problem, are presented to illustrate the efficiency of the proposed method.
49.1NAApr 7
On convergence of residual-based extended randomized Kaczmarz methods for matrix equationsWendi Bao, Jing Li, Lili Xing et al.
In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. A feasible range for the momentum parameters is determined. Numerical experiments demonstrate that the proposed methods are much more effective than the existing ones, especially the method with momentum.