@Article{NMTMA-11-140,
author = {Baohua Huang and Changfeng Ma},
title = {Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2018},
volume = {11},
number = {1},
pages = {140--159},
abstract = {<p style="text-align: justify;">The purpose of this paper is to derive the generalized conjugate residual (GCR) algorithm for finding the
least squares solution on a class of Sylvester matrix equations. We prove that if the system is inconsistent, the least squares solution can be obtained with infinite iterative steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrix to obtain the minimum norm least squares solutionof the problem. Finally, we give some numerical examples to illustrate the performance of GCR algorithm.</p><p><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12px;"></span></p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2017-0010},
url = {http://global-sci.org/intro/article_detail/nmtma/10647.html}
}