Residual norm steepest descent based iterative algorithms for Sylvester tensor equations

Consider the following consistent Sylvester tensor equation\[\mathscr{X}\times_۱ A +\mathscr{X}\times_۲ B+\mathscr{X}\times_۳ C=\mathscr{D},\]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.

کلیدواژه ها:

Sylvester tensor equation ، iterative algorithm ، Convergence