On convergence of residual-based extended randomized Kaczmarz methods for matrix equations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914451855245312 |
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| author | Bao, Wendi Li, Jing Xing, Lili Li, Weiguo Wang, Jichao |
| author_facet | Bao, Wendi Li, Jing Xing, Lili Li, Weiguo Wang, Jichao |
| contents | In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. A feasible range for the momentum parameters is determined. Numerical experiments demonstrate that the proposed methods are much more effective than the existing ones, especially the method with momentum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05726 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On convergence of residual-based extended randomized Kaczmarz methods for matrix equations Bao, Wendi Li, Jing Xing, Lili Li, Weiguo Wang, Jichao Numerical Analysis In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. A feasible range for the momentum parameters is determined. Numerical experiments demonstrate that the proposed methods are much more effective than the existing ones, especially the method with momentum. |
| title | On convergence of residual-based extended randomized Kaczmarz methods for matrix equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.05726 |