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On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation

Author

Listed:
  • Lili Xing

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Wendi Bao

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Weiguo Li

    (College of Science, China University of Petroleum, Qingdao 266580, China)

Abstract

A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation A X B = C , where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved that these methods converge to the solution or least-square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations.

Suggested Citation

  • Lili Xing & Wendi Bao & Weiguo Li, 2023. "On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation," Mathematics, MDPI, vol. 11(21), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4554-:d:1274431
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    References listed on IDEAS

    as
    1. Liu, Zhongyun & Li, Zhen & Ferreira, Carla & Zhang, Yulin, 2020. "Stationary splitting iterative methods for the matrix equation AXB=C," Applied Mathematics and Computation, Elsevier, vol. 378(C).
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