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

Abstract

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.