English

The sparse Kaczmarz method with surrogate hyperplane for the regularized basis pursuit problem

Numerical Analysis 2024-06-24 v1 Numerical Analysis

Abstract

The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of residual-based surrogate hyperplane sparse Kaczmarz method is introduced and the implementations are well discussed. Their convergence theories are proved and the linear convergence rates are studied and compared in details. Numerical experiments verify the efficiency of the proposed methods.

Keywords

Cite

@article{arxiv.2406.15082,
  title  = {The sparse Kaczmarz method with surrogate hyperplane for the regularized basis pursuit problem},
  author = {Ze Wang and Jun-Feng Yin and Ji-Chen Zhao},
  journal= {arXiv preprint arXiv:2406.15082},
  year   = {2024}
}
R2 v1 2026-06-28T17:14:39.286Z