On the *-Sylvester equation AX +/- X* B* = C

Chun-Yueh Chiang, King-Wah Eric Chu, Wen-wei Lin

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We consider the solution of the star-Sylvester equations AX +/- (XB star)-B-star = C, for star = T, H and A, B, is an element of C-nxn, and the related linear matrix equations AXB(star) +/- X-star = C, AXB(star) +/- (CXD star)-D-star = E and AX +/- X(star)A(star) = 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.
Original languageEnglish
Pages (from-to)8393 - 8407
Number of pages15
JournalApplied Mathematics and Computation
Issue number17
Publication statusPublished - 2012

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