A hierarchical gradient based iterative algorithm of [L. Xie et al.,
Computers and Mathematics with Applications 58 (2009) 1441-1448] has been
presented for finding the numerical solution for general linear matrix
equations, and the convergent factor has been discussed by numerical
experiments. However, they pointed out that how to choose a best convergence
factor is still a project to be studied. In this paper, we discussed the
optimal convergent factor for the gradient based iterative algorithm and
obtained the optimal convergent factor. Moreover, the theoretical results of
this paper can be extended to other methods of gradient-type based. Results
of numerical experiments are consistent with the theoretical findings.
A Fast Gradient-Based Iterative Algorithm for Undersampled Phase Retrieval
