The Projected Generalized Sylvester Equations: Numerical Solution and Applications

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Abstract: In this paper we consider the numerical solution of large-scale projected generalized continuous-time and discrete-time Sylvester equations with low-rank right-hand sides. First, we present the results on the sufficient conditions for the existence, uniqueness, and analytic formula of the solutions of these equations. Second, we review the low-rank alternating direction implicit method and the low-rank cyclic Smith method for solving the projected generalized continuous-time Sylvester equation, and propose a numerical method for the projected generalized discrete-time Sylvester equation. Third, we show that the solutions of these two equations are useful for computing the HL2 inner product of two descriptor systems. Finally, we present some numerical experiments.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 15, 2016, Art. #9

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Yiqin Lin, Liang Bao, "The Projected Generalized Sylvester Equations: Numerical Solution and Applications," WSEAS Transactions on Mathematics, vol. 15, pp. 83-95, 2016, DOI:
Yiqin Lin, Liang Bao. The Projected Generalized Sylvester Equations: Numerical Solution and Applications. WSEAS Transactions on Mathematics. 2016;15:83-95.
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