On the ★-Sylvester equation AX ± X ★ B ★ = C

Abstract: We consider the solution of the ★-Sylvester equations AX ± X ★ B ★ = C, for ★= T, H and , and the related linear matrix equations AXB ★ ± X ★ = C, AXB ★ ± CX ★ D ★ = E and AX ± X ★ A ★ = C. Solvability conditions and numerical methods are considered, in terms of the (generalized and periodic) Schur and QR decompositions. We emphasize the square cases where m = n but the rectangular cases will be considered. [Copyright &y& Elsevier]