Some remarks on Jacobi and Gauss–Seidel-type iteration methods for the matrix equation AXB=C

摘要

Tian, et al. proposed in [5] several Jacobi and Gauss–Seidel-type iterative methods for solving matrix equation AXB=C. Those methods were demonstrated to be effective by the given numerical experiments. However, we find that there is a technical error in the proof of the main theorem (Theorem 3.3). In this note we first show this erratum by an example. Then we establish a new convergence theorem which contains the Theorem 3.3 in [5] as a special case.