An Alternating Direction Implicit Method for Solving Projected Generalized Continuous-Time Sylvester Equations

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Yiqin Lin 1,* Liang Bao 2

1. Department of Mathematics and Computational Science Hunan University of of Science and Engineering Yongzhou 425100, P. R. China

2. Department of Mathematics East China University of Science and Technology Shanghai, 200237, P. R. China

* Corresponding author.


Received: 20 Aug. 2011 / Revised: 1 Oct. 2011 / Accepted: 28 Oct. 2011 / Published: 5 Dec. 2011

Index Terms

Projected generalized Sylvester equations, Alternating direction implicit method, Low-rank approximate solution, C-stable


In this paper we propose a low-rank alternating direction implicit (ADI) method to solve projected generalized continuous-time Sylvester equations with low-rank right-hand sides. Such equations arise in control theory including the computation of inner products and norms, and the model reduction based on balanced truncation for descriptor systems. The requirements of this method are moderate with respect to both computational cost and memory. Numerical experiments presented in this paper show the effectiveness of the proposed method.

Cite This Paper

Yiqin Lin,Liang Bao,"An Alternating Direction Implicit Method for Solving Projected Generalized Continuous-Time Sylvester Equations", IJEM, vol.1, no.6, pp.64-71, 2011. DOI: 10.5815/ijem.2011.06.10


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