The gradient-based iteration (GBI) method is widely utilized for solving large-scale matrix equations \(AXB=C\) due to its simplicity and efficiency. This paper proposes significant enhancements to the convergence rate of the GBI method by integrating preconditioned technique, momentum acceleration, and Chebyshev semi-iterative scheme. We give rigorous convergence analyses for these accelerated methods and provide detailed investigations into optimal parameter selection. Finally, comprehensive numerical experiments are carried out to demonstrate the superior efficiency of the accelerated methods with the corresponding optimal parameters. In addition, their potential utility is illustrated through the real-world applications, such as tensor surface fitting in computer-aided geometric design.
