Scholarlink

<p>In this work, we propose a class of surrogate hyperplane Kaczmarz methods with oblique projection for solving linear systems. Two ingredients are crucial to the success of the proposed method, that is, the oblique projection direction and the weight vector for generating the surrogate hyperplane at each iteration. To this end, we first derive an optimal oblique projection direction, and then suggest a way of selecting the weight vector, by which we formulate our residual-based surrogate hyperplane Kaczmarz method with oblique projection, abbreviated as RSHKO. The convergence analysis of the RSHKO method is studied. Numerical experiments are reported for confirming the validity of theoretical analysis and comparing the numerical performance with some of existing variants of 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

A surrogate hyperplane Kaczmarz method with oblique projection for solving linear systems

  • 期刊论文

  • 发表日期：

    2025年7月24日

查看全文
  • Zeyu Dong,
  • Shiyang Qin,
  • Guojian Yin,
  • Jun-Feng Yin,
  • Ning Zheng

摘要

In this work, we propose a class of surrogate hyperplane Kaczmarz methods with oblique projection for solving linear systems. Two ingredients are crucial to the success of the proposed method, that is, the oblique projection direction and the weight vector for generating the surrogate hyperplane at each iteration. To this end, we first derive an optimal oblique projection direction, and then suggest a way of selecting the weight vector, by which we formulate our residual-based surrogate hyperplane Kaczmarz method with oblique projection, abbreviated as RSHKO. The convergence analysis of the RSHKO method is studied. Numerical experiments are reported for confirming the validity of theoretical analysis and comparing the numerical performance with some of existing variants of Kaczmarz method.