Scholarlink

<p>This paper addresses the challenge of solving large-scale nonlinear equations with Hölder continuous Jacobians. We introduce a novel incremental Gauss–Newton (IGN) method with an explicit superlinear convergence rate, which outperforms existing incremental methods that only achieve linear convergence rates. In particular, we formulate our problem using the nonlinear least squares with finite-sum structure, and our method updates incrementally by utilizing information from one component in each round. We also provide a mini-batch extension to our IGN method that obtains an even faster superlinear convergence rate. Furthermore, we conduct numerical experiments to show the advantages of the proposed methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Incremental Gauss–Newton Methods with Superlinear Convergence Rates

  • 期刊论文

  • 发表日期：

    2026年5月25日

查看全文
  • Zhiling Zhou,
  • Zhuanghua Liu,
  • Chengchang Liu,
  • Luo Luo

摘要

This paper addresses the challenge of solving large-scale nonlinear equations with Hölder continuous Jacobians. We introduce a novel incremental Gauss–Newton (IGN) method with an explicit superlinear convergence rate, which outperforms existing incremental methods that only achieve linear convergence rates. In particular, we formulate our problem using the nonlinear least squares with finite-sum structure, and our method updates incrementally by utilizing information from one component in each round. We also provide a mini-batch extension to our IGN method that obtains an even faster superlinear convergence rate. Furthermore, we conduct numerical experiments to show the advantages of the proposed methods.