The BCR algorithms for solving the reflexive or anti-reflexive solutions of generalized coupled Sylvester matrix equations

This paper proposes the Lanczos version of the biconjugate residual algorithm to solve the reflexive or anti-reflexive solutions of a class of generalized coupled Sylvester matrix equations. We give a convergence analysis, and by constructing a special form of the initial matrices, the minimum-norm reflexive solutions can be obtained through finite-step iterations without considering rounding errors. At the end of the paper, we provide numerical examples to illustrate the feasibility and effectiveness of this algorithm. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.