On the parameterized two-step iteration method for solving the matrix equation AXB = C

Zhaolu Tian, Yudong Wang, Nian-Ci Wu and Zhongyun Liu

Applied Mathematics and Computation, 2024, vol. 464, issue C

Abstract: In this paper, based on the iteration framework [10], by introducing two tuning parameters α,β in the splittings of the matrices A and B, a parameterized two-step iteration (PTSI) method is presented for solving the matrix equation AXB=C. In the sequel, the convergence property and choices of the parameters α,β are analyzed in detail. For some special cases of the matrices A and B, the corresponding PTSI methods are also investigated, and the optimal parameters α,β can be obtained for the symmetric positive definite (SPD) matrices A and B. In addition, some comparison results of the PTSI method are given for the M-matrices A,B compared with the TSI method [10]. Finally, several numerical examples are performed to verify the efficiencies of the PTSI method and choices of the optimal parameters.

Keywords: SPD matrix; M-matrix; Two-step iteration; Optimal parameter; Regular splitting (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005702

DOI: 10.1016/j.amc.2023.128401

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