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Multi-shift quadratic alternating direction implicit iteration for high-speed positive-real balanced truncation

Published: 24 July 2006 Publication History

Abstract

This paper presents a multi-shift generalization of the recently proposed quadratic alternating direction implicit (QADI) iteration. QADI and its Cholesky Factor (CF) variant, CFQADI, have been shown to be efficient ways of solving the large-scale algebraic Riccati equations (AREs) required in positive-real balanced truncation (PRBT). However, only their single-shift implementations have been considered so far. Using linear fractional transformation (LFT), we present elegant multi-shift extensions of both QADI and CFQADI, thereby enabling even faster and more accurate PRBT.

References

[1]
J. R. Phillips, L. Daniel, and L M. Silveira, "Guaranteed passive balancing transformations for model order reduction," IEEE Trans. Computer-Aided Design, vol. 22, no. 8, pp. 1027--1041, Aug. 2003.
[2]
N. Wong and V. Balakrishnan, "Fast balanced stochastic truncation via a quadratic extension of the alternating direction implicit iteration," in Proc. IEEE Int. Conf. Computer-Aided Design, Nov. 2005, pp. 801--805.
[3]
T. Penzl, "A cyclic low rank Smith method for large sparse Lyapunov equations with applications in model reduction and optimal control," SIAM J. SCI. COMPUT., vol. 21, no. 4, pp. 1401--1418, 2000.
[4]
P. Benner, E. S. Quintana-Ortí, and G. Quintana-Ortí, "Efficient numerical algorithms for balanced stochastic truncation," Int. J. Appl. Math. Comp. Sci., vol. 11, pp. 1123--1150, 2001.
[5]
J. Li and J. White, "Low-rank solution of Lyapunov equations," SIAM Review, vol. 46, no. 4, pp. 693--713, 2004.
[6]
H. Weiss, Q. Wang, and J. L. Speyer, "System characterization of positive real conditions," IEEE Trans. Automat. Contr., vol. 39, no. 3, pp. 540--544, Mar. 1994.
[7]
K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice-Hall, 1996.
[8]
E. Wachspress, "The ADI minimax problem for complex spectra," Appl. Math Lett., vol. 1, pp. 311--314, 1988.
[9]
A. Odabasioglu, M. Celik, and L. T. Pileggi, "PRIMA: Passive reduced-order interconnect macromodeling algorithm," IEEE Trans. Computer-Aided Design, vol. 17, no. 8, pp. 645--654, Aug. 1998.

Cited By

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  • (2007)Fast positive-real balanced truncation of symmetric systems using cross Riccati equationsProceedings of the conference on Design, automation and test in Europe10.5555/1266366.1266695(1496-1501)Online publication date: 16-Apr-2007
  • (2007)Passivity-preserving model order reduction of linear time-varying macromodels2007 7th International Conference on ASIC10.1109/ICASIC.2007.4415885(1334-1339)Online publication date: Oct-2007
  • (2007)Fast Positive-Real Balanced Truncation of Symmetric Systems Using Cross Riccati Equations2007 Design, Automation & Test in Europe Conference & Exhibition10.1109/DATE.2007.364512(1-6)Online publication date: Apr-2007

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cover image ACM Conferences
DAC '06: Proceedings of the 43rd annual Design Automation Conference
July 2006
1166 pages
ISBN:1595933816
DOI:10.1145/1146909
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 24 July 2006

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Author Tags

  1. ADI
  2. balanced truncation
  3. model order reduction
  4. positive real

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DAC06
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DAC06: The 43rd Annual Design Automation Conference 2006
July 24 - 28, 2006
CA, San Francisco, USA

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Overall Acceptance Rate 1,770 of 5,499 submissions, 32%

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Cited By

View all
  • (2007)Fast positive-real balanced truncation of symmetric systems using cross Riccati equationsProceedings of the conference on Design, automation and test in Europe10.5555/1266366.1266695(1496-1501)Online publication date: 16-Apr-2007
  • (2007)Passivity-preserving model order reduction of linear time-varying macromodels2007 7th International Conference on ASIC10.1109/ICASIC.2007.4415885(1334-1339)Online publication date: Oct-2007
  • (2007)Fast Positive-Real Balanced Truncation of Symmetric Systems Using Cross Riccati Equations2007 Design, Automation & Test in Europe Conference & Exhibition10.1109/DATE.2007.364512(1-6)Online publication date: Apr-2007

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