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On Convergence Behavior of Randomized Kaczmarz-type Methods for Solving Doubly Noisy Linear Systems — arXiv:2608.22259

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.22259
License (as archived): CC0-1.0
Archived: 2026-10-18T08:27:35.558Z
SHA-256 of the archived text: 5d1562027184857dbda050b7fae653755c3047966ea7d4306c51e9d29a5925e2
Stable URL of this page: https://metraipolis.com/documento/dc_c2e367a4cebe

How to cite

On Convergence Behavior of Randomized Kaczmarz-type Methods for Solving Doubly Noisy Linear Systems — arXiv:2608.22259 — arXiv (en), https://arxiv.org/abs/2608.22259 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c2e367a4cebe (Metraipolis archive dc_c2e367a4cebe, sha256 5d1562027184857dbda050b7fae653755c3047966ea7d4306c51e9d29a5925e2)

BibTeX

@misc{dcc2e367a4cebe,
  title = {On Convergence Behavior of Randomized Kaczmarz-type Methods for Solving Doubly Noisy Linear Systems — arXiv:2608.22259},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.22259},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c2e367a4cebe; sha256 5d1562027184857dbda050b7fae653755c3047966ea7d4306c51e9d29a5925e2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.22259. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we consider the convergence of some popular Kaczmarz-type methods, including the randomized Kaczmarz (RK) method, the randomized extended Kaczmarz (REK) method, the randomized block Kaczmarz (RBK) method, and the randomized double block Kaczmarz (RDBK) method for doubly noisy linear system. To the best of our knowledge, this is the first work that considers and compares the convergence of the Kaczmarz-type methods for consistent linear systems, as well as that for inconsistent linear systems to solve double noisy linear system. We prove that these methods converge to a neighborhood of the smallest norm least squares solution of the underlying noiseless system. Specifically, RK and RBK that are designed for consistent linear systems, often outperform REK and RDBK that are designed for inconsistent linear systems, respectively, in terms of the convergence rate or the convergence horizon. Moreover, we establish the convergence of the more general sketch-and-project framework for the doubly noisy linear system. The analysis provides more comprehensive results without imposing any additional restrictions. Numerical experiments are performed to validate our theoretical results.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.22259 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T08:27:23.839Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).