Residual norm steepest descent based iterative algorithms for Sylvester tensor equations

Consider the following consistent Sylvester tensor equation
X×1A×2B×3C=D,
where the matrices A,B,C and the tensor D are given and X is the unknown tensor. The current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and its modified version for solving the mentioned Sylvester tensor equation without setting the restriction of the existence of a unique solution. Numerical experiments are reported which confirm the validity of the presented results.