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Multi-step Partially Randomized Extended Kaczmarz Algorithm For Solving Inconsistent Linear Systems.

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Title: Multi-step Partially Randomized Extended Kaczmarz Algorithm For Solving Inconsistent Linear Systems.
Authors: Guo, Ying-Ying1 guoyy99910@163.com
Source: IAENG International Journal of Applied Mathematics. Mar2026, Vol. 56 Issue 3, p994-1000. 7p.
Subjects: Linear systems, Iterative methods (Mathematics), Numerical analysis, Computer performance
Abstract: This paper introduces a multi-step partially randomized extended Kaczmarz (MPREK) method, which employs a residual-threshold-based row selection strategy to adaptively identify the most influential rows in each iteration. This approach removes the need for preset inner-loop parameters while preserving convergence guarantees. Numerical tests conducted on both synthetic and actual datasets reveal that MPREK consistently outperforms some other REK-type algorithms in both iteration counts and CPU time, providing an effective balance between efficiency and convergence speed. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Multi-step Partially Randomized Extended Kaczmarz Algorithm For Solving Inconsistent Linear Systems.
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  Data: <searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+performance%22">Computer performance</searchLink>
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  Data: This paper introduces a multi-step partially randomized extended Kaczmarz (MPREK) method, which employs a residual-threshold-based row selection strategy to adaptively identify the most influential rows in each iteration. This approach removes the need for preset inner-loop parameters while preserving convergence guarantees. Numerical tests conducted on both synthetic and actual datasets reveal that MPREK consistently outperforms some other REK-type algorithms in both iteration counts and CPU time, providing an effective balance between efficiency and convergence speed. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        PageCount: 7
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        Type: general
      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Numerical analysis
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      – TitleFull: Multi-step Partially Randomized Extended Kaczmarz Algorithm For Solving Inconsistent Linear Systems.
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              Text: Mar2026
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