scholarly journals Fast Positive-Real Balanced Truncation Via Quadratic Alternating Direction Implicit Iteration

Author(s):  
Ngai Wong ◽  
Venkataramanan Balakrishnan
2020 ◽  
Vol 2 (1) ◽  
pp. 1-13
Author(s):  
Linus Balicki

The low-rank alternating direction implicit (LR-ADI) iteration is an effective method for solving large-scale Lyapunov equations. In the software library pyMOR, solutions to Lyapunov equations play an important role when reducing a model using the balanced truncation method. In this article we introduce the LR-ADI iteration as well as pyMOR, while focusing on its features which are relevant for integrating the iteration into the library. We compare the run time of the iteration's pure pyMOR implementation with those achieved by external libraries available within the pyMOR framework.


2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yujian Zhou ◽  
Liang Bao ◽  
Yiqin Lin

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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