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

Lili Xing, Wendi Bao and Weiguo Li ()
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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

Mathematics, 2023, vol. 11, issue 21, 1-15

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.

Keywords: matrix equation; randomized block Kaczmarz; randomized extended block Kaczmarz; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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