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December 9, 2025Mathematics of Computation

On adaptive stochastic extended iterative methods for solving least squares

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Authors

YZYun ZengKunming Medical UniversityDHDeren HanBeihang UniversityYSYansheng SuPeople 's Liberation Army 451 Hospital

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Implication

Novel adaptive stochastic methods improve least squares solutions in linear systems, indicating better convergence results.

Key Points

  • To develop an adaptive stochastic extended iterative method for solving least squares problems in linear systems.
  • Introduced an adaptive stochastic extended iterative method based on the Kaczmarz method
  • Presented three equivalent stochastic reformulations of the least squares problem
  • Employed adaptive variants of stochastic heavy ball momentum (SHBM) for optimization.
  • Proved convergence of the method with R-linearly expected outcomes
  • Demonstrated advantages of the adaptive method over nonadaptive methods through numerical experiments.

Cite This Study

Zeng et al. (2025) studied this question.

synapsesocial.com/papers/69401d732d562116f28f94ebhttps://doi.org/10.1090/mcom/4168
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