TY - JOUR T1 - Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 140 EP - 159 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0010 UR - https://global-sci.org/intro/article_detail/nmtma/10647.html KW - Sylvester matrix equation, Least squares solution, Generalized conjugate residual algorithm, Numerical experiments. AB -
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.