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<p>In this paper, we employ two preconditioned general splitting methods to study the split feasibility problem. One is the preconditioned linear relaxed splitting method and the other is a preconditioned method that combines the alternating inertial step with the former. The methods employ a novel step-size strategy, which does not require any prior knowledge about the operator norm. Moreover, we also provide a convergence analysis of our algorithm under appropriate parameters. Finally, in a numerical experiment, we apply algorithms to solve a signal recovery problem. Compared with existing non-preconditioned algorithms, the numerical experiments demonstrate the effectiveness of our proposed methods.</p>

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Preconditioning splitting methods for the split feasibility problem

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • Wenkai Guo,
  • Linlin Feng,
  • Luoyi Shi,
  • Yasong Chen

摘要

In this paper, we employ two preconditioned general splitting methods to study the split feasibility problem. One is the preconditioned linear relaxed splitting method and the other is a preconditioned method that combines the alternating inertial step with the former. The methods employ a novel step-size strategy, which does not require any prior knowledge about the operator norm. Moreover, we also provide a convergence analysis of our algorithm under appropriate parameters. Finally, in a numerical experiment, we apply algorithms to solve a signal recovery problem. Compared with existing non-preconditioned algorithms, the numerical experiments demonstrate the effectiveness of our proposed methods.