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

2011 ◽  
Vol 1 (6) ◽  
pp. 64-71
Author(s):  
Yiqin Lin ◽  
Liang Bao
Keyword(s):  
Continuous Time ◽  
Implicit Method ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Alternating Direction

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

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yujian Zhou ◽  
Liang Bao ◽  
Yiqin Lin
Keyword(s):  
Continuous Time ◽  
Computational Cost ◽  
Implicit Method ◽  
Descriptor Systems ◽  
Low Rank ◽  
Balanced Truncation ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Smith Method ◽  
Alternating Direction

We present the generalized low-rank alternating direction implicit method and the low-rank cyclic Smith 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 andℍ2norms and the model reduction based on balanced truncation for descriptor systems. The requirements of these methods are moderate with respect to both computational cost and memory. Numerical experiments presented in this paper show the effectiveness of the proposed methods.

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