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<p>In this paper, we propose a double stochastic block method for solving nonlinear systems (DSBN), which unifies some stochastic row-block and column-block methods in a unified framework. Convergence analysis of the new algorithm is established based on local tangential cone conditions. Furthermore, to reduce the computations of the Jacobian matrix in random probabilities, a stochastic column-block method (SCBN) with uniform probabilities is established for solving nonlinear systems, and its convergence is investigated. Finally, numerical experiments are present to verify the effectiveness of the proposed methods.</p>

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On stochastic block methods for solving nonlinear equations

  • 期刊论文

  • 发表日期：

    2025年2月15日

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  • Wendi Bao,
  • Zhiwei Guo,
  • Lili Xing,
  • Weiguo Li

摘要

In this paper, we propose a double stochastic block method for solving nonlinear systems (DSBN), which unifies some stochastic row-block and column-block methods in a unified framework. Convergence analysis of the new algorithm is established based on local tangential cone conditions. Furthermore, to reduce the computations of the Jacobian matrix in random probabilities, a stochastic column-block method (SCBN) with uniform probabilities is established for solving nonlinear systems, and its convergence is investigated. Finally, numerical experiments are present to verify the effectiveness of the proposed methods.