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Mathematics > Numerical Analysis

arXiv:2210.02602 (math)
[Submitted on 5 Oct 2022]

Title:Convergence rates of the Kaczmarz-Tanabe method for linear systems

Authors:Chuan-gang Kang
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Abstract:In this paper, we investigate the Kaczmarz-Tanabe method for exact and inexact linear systems. The Kaczmarz-Tanabe method is derived from the Kaczmarz method, but is more stable than that. We analyze the convergence and the convergence rate of the Kaczmarz-Tanabe method based on the singular value decomposition theory, and discover two important factors, i.e., the second maximum singular value of $Q$ and the minimum non-zero singular value of $A$, that influence the convergence speed and the amplitude of fluctuation of the Kaczmarz-Tanabe method (even for the Kaczmarz method). Numerical tests verify the theoretical results of the Kaczmarz-Tanabe method.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2210.02602 [math.NA]
  (or arXiv:2210.02602v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.02602

Submission history

From: Chuan-Gang Kang [view email]
[v1] Wed, 5 Oct 2022 23:22:11 UTC (5,782 KB)
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