Scholarlink

<p>The residual norm steepest descent method is favorable for solving linear systems when its coefficient matrix is nonsingular, but is infeasible for overdetermined and underdetermined cases, while the randomized block Kaczmarz methods are powerful for solving the two cases, but converge slower in general. In this paper, followed by the blocks determined by the <i>k</i>-means clustering, a randomized block residual steepest descent method, which incorporates the residual norm steepest descent with the randomized block Kaczmarz method, is proposed for solving the general large sparse linear systems. Theoretical analysis demonstrates that the proposed method converges to an exact solution with the expected exponential rate. Numerical experiments, including some generated random data and image processing, are performed to illustrate the effectiveness of the new method compared to a state-of-the-art randomized block Kaczmarz method.</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

Randomized block residual steepest descent method with k-means clustering for large sparse linear systems

  • 期刊论文

  • 发表日期：

    2025年5月19日

查看全文
  • Tao Li,
  • Liang Li,
  • Xin-Fang Zhang

摘要

The residual norm steepest descent method is favorable for solving linear systems when its coefficient matrix is nonsingular, but is infeasible for overdetermined and underdetermined cases, while the randomized block Kaczmarz methods are powerful for solving the two cases, but converge slower in general. In this paper, followed by the blocks determined by the k-means clustering, a randomized block residual steepest descent method, which incorporates the residual norm steepest descent with the randomized block Kaczmarz method, is proposed for solving the general large sparse linear systems. Theoretical analysis demonstrates that the proposed method converges to an exact solution with the expected exponential rate. Numerical experiments, including some generated random data and image processing, are performed to illustrate the effectiveness of the new method compared to a state-of-the-art randomized block Kaczmarz method.