Solving the system of linear operator equations over generalized bisymmetric matrices
Masoud Hajarian · Transactions of the Institute of Measurement and Control · 2013
This paper proposes an iterative method based on the conjugate gradient method on the normal equations for finding the generalized bisymmetric solution [Formula: see text] to the system of linear operator equations [Formula: see text] where [Formula: see text] are linear operators. By the iterative method, the solvability of this system over the generalized bisymmetric matrix [Formula: see text] can be determined automatically. When the system of linear operator equations is consistent over the generalized bisymmetric matrix [Formula: see text], the iterative method with any generalized bisymmetric initial iterative matrix [Formula: see text] can compute the generalized bisymmetric solution within a finite number of iterations in the absence of roundoff errors. In addition, by the proposed iterative method, the least Frobenius norm generalized bisymmetric solution can be derived when a special initial generalized bisymmetric matrix is chosen. Finally, two numerical examples are presented to support the theoretical results of this paper.