A modified gradient-based algorithm for solving extended Sylvester-conjugate matrix equations

In this paper, we present a modified gradient-based algorithm for solving extended Sylvester-conjugate matrix equations. The idea is from the gradient-based method introduced in [14] and the relaxed gradient-based algorithm proposed in [16]. The convergence analysis of the algorithm is investigated. We show that the iterative solution converges to the exact solution for any initial value based on some appropriate assumptions. A numerical example is given to illustrate the effectiveness of the proposed method and to test its efficiency and accuracy compared with those presented in [14] and [16].