A minimal residual algorithm for the inconsistent matrix equation \(AXB = C\) over symmetric matrices (Q2371462)

The authors consider the problem of solving the nearness problem associated with the inconsistent matrix equation \(AXB=C\), for symmetric matrices. An iterative method with short recurrences was presented by \textit{Zhen-yun Peng} [ibid. 170, 711--723 (2005; Zbl 1081.65039)]. However this algorithm may be slow in case of the irregular convergence behavior in the residual norm of \(AXB=C\). In order to remedy this problem, the authors present a modification based on the idea of the classical conjugate gradient (CG) method. This CG-type method can both maintain the short recurrences and satisfy a minimization property, i.e., the approximate solution minimizes the residual norm over a special affine subspace, which ensures that this method possesses a more smooth convergence than the original method presented by Peng. In addition, an error bound is given and numerical experiments are reported.