On the w-Sylvester equation AX ± X w B w = C
Chun-Yueh Chiang, Eric King‐wah Chu, Wen‐Wei Lin · 2012
We consider the solution of the w-Sylvester equations AX ± X w B w = C, for w = T, H and A; B;2 C nn , and the related linear matrix equations AXB w ± X w = C, AXB w ± CX w D w = E and AX ± X w A w = 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.