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 - <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>