2022/09/13 by Yanjun Zhang, Hanyu Li, Zhang, Yanjun +3 · 1 citation
Computer Science · Engineering · #FOS: Mathematics #Face and Expression Recognition #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2209.06082
openalex publication_date 2022/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The nonlinear Kaczmarz method was recently proposed to solve the system of nonlinear equations. In this paper, we first discuss two greedy selection rules, i.e., the maximum residual and maximum distance rules, for the nonlinear Kaczmarz iteration. Then, based on them, two kinds of greedy randomized sampling methods are presented. Further, we also devise four corresponding greedy randomized block methods, i.e., the multiple samples-based methods. The linear convergence in expectation of all the proposed methods is proved. Numerical results show that, in some applications including brown almost linear function and generalized linear model, the greedy selection rules give faster convergence rates than the random ones, and the block methods outperform the single sample-based ones.