On RGI Algorithms for Solving Sylvester Tensor Equations

This paper is concerned with studying the relaxed gradient-based iterative method based on tensor format to solve Sylvester equation. From information given by previous steps, we further develop a modified which converges faster than above. Under some suitable conditions, prove that introduced methods are convergent unique solution for any initial tensor. At last, provide numerical examples show our perform much better GI algorithm proposed Chen and Lu (Math. Probl. Eng. 2013) both in number of iteration steps elapsed CPU time.