IEICE TRANSACTIONS on Fundamentals
Real Cholesky Factor-ADI Method for Low-Rank Solution of Projected Generalized Lyapunov Equations
Summary :
The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky factor is represented in a real form so that it is useful for balanced truncation of sparsely connected RLC networks. Moreover, we show how to determine the shift parameters which are required for the ADI iterations, where Krylov subspace method is used for finding the shift parameters that reduce the residual error quickly. In the illustrative examples, we confirm that the real Cholesky factor certainly provides low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. Effectiveness of the shift parameters determined by Krylov subspace method is also demonstrated.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.3 pp.702-709
- Publication Date
- 2016/03/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.702
- Type of Manuscript
- PAPER
- Category
- Nonlinear Problems
Authors
Yuichi TANJI
Kagawa University
Keyword
Latest Issue
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Yuichi TANJI, "Real Cholesky Factor-ADI Method for Low-Rank Solution of Projected Generalized Lyapunov Equations" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 3, pp. 702-709, March 2016, doi: 10.1587/transfun.E99.A.702.
Abstract: The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky factor is represented in a real form so that it is useful for balanced truncation of sparsely connected RLC networks. Moreover, we show how to determine the shift parameters which are required for the ADI iterations, where Krylov subspace method is used for finding the shift parameters that reduce the residual error quickly. In the illustrative examples, we confirm that the real Cholesky factor certainly provides low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. Effectiveness of the shift parameters determined by Krylov subspace method is also demonstrated.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.702/_p
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@ARTICLE{e99-a_3_702,
author={Yuichi TANJI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Real Cholesky Factor-ADI Method for Low-Rank Solution of Projected Generalized Lyapunov Equations},
year={2016},
volume={E99-A},
number={3},
pages={702-709},
abstract={The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky factor is represented in a real form so that it is useful for balanced truncation of sparsely connected RLC networks. Moreover, we show how to determine the shift parameters which are required for the ADI iterations, where Krylov subspace method is used for finding the shift parameters that reduce the residual error quickly. In the illustrative examples, we confirm that the real Cholesky factor certainly provides low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. Effectiveness of the shift parameters determined by Krylov subspace method is also demonstrated.},
keywords={},
doi={10.1587/transfun.E99.A.702},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - Real Cholesky Factor-ADI Method for Low-Rank Solution of Projected Generalized Lyapunov Equations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 702
EP - 709
AU - Yuichi TANJI
PY - 2016
DO - 10.1587/transfun.E99.A.702
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2016
AB - The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky factor is represented in a real form so that it is useful for balanced truncation of sparsely connected RLC networks. Moreover, we show how to determine the shift parameters which are required for the ADI iterations, where Krylov subspace method is used for finding the shift parameters that reduce the residual error quickly. In the illustrative examples, we confirm that the real Cholesky factor certainly provides low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. Effectiveness of the shift parameters determined by Krylov subspace method is also demonstrated.
ER -
English
