In this paper, inspired by the modified relaxed gradient-based iterative (MRGI) algorithm proposed by Huang et al. (Numer. Algorithms 97(4), 1955–2009 (2024)), a modified Jacobi gradient iterative (MJGI) algorithm is developed to solve the complex conjugate transpose Sylvester matrix equation through updates and modifications. Specifically, we replace the original full matrices by extracting the diagonal parts of the matrices \(A_i\) and \(B_i\) , while proposing a progressive update mechanism with hybrid historical iterative values. This mechanism dynamically integrates the newly computed subblocks with the global historical values Y(l) during the updating process. By retaining the memory effect of historical information, we enhance the algorithmic accuracy. Furthermore, we establish an \(\omega\) -parameterized convergence factor optimization framework that significantly accelerates the convergence rate. Theoretical analysis, grounded in the real representation of matrices and Kronecker product operations, establishes the convergence conditions of the algorithm and determines explicit optimization ranges for the relaxation factor and step size parameters. The numerical example demonstrates that the MJGI algorithm outperforms the MRGI algorithm in terms of iteration counts and CPU running time, especially under high-precision requirements (residual threshold \(\tau \le 10^{-6}\) ), with an improvement in iteration efficiency, defined as the number of iterations required to achieve a specified residual threshold, by more than 76. 31%.
