Residual norm steepest descent based iterative algorithms for Sylvester tensor equations

Document Type : Research Article



Consider the following consistent Sylvester tensor equation
\[\mathscr{X}\times_1 A +\mathscr{X}\times_2 B+\mathscr{X}\times_3 C=\mathscr{D},\]
where the matrices $A,B, C$ and the tensor $\mathscr{D}$ are given and $\mathscr{X}$ 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.