Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Krylov subspace methods for large-scale matrix problems in control
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Developing Bi-CG and Bi-CR methods to solve generalized Sylvester-transpose matrix equations
International Journal of Automation and Computing
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In this paper, we propose a new algorithm to solve the Sylvester matrix equation XA+BX=C. The technique consists of orthogonal reduction of the matrix A to a block upper Hessenberg form P^TAP=H and then solving the reduced equation, YH+BY=C for Y through recurrence relation, where Y=XP, and C^'=CP. We then recover the solution of the original problem via the relation X=YP^T. The numerical results show the accuracy and the efficiency of the proposed algorithm. In addition, how the technique described can be applied to other matrix equations was shown.