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An improved numerical method for balanced truncation for symmetric second-order systems.

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Title: An improved numerical method for balanced truncation for symmetric second-order systems.
Authors: Benner, Peter1 (AUTHOR), Kürschner, Patrick1 (AUTHOR) kuerschner@mpi-magdeburg.mpg.de, Saak, Jens1 (AUTHOR)
Source: Mathematical & Computer Modelling of Dynamical Systems. Dec2013, Vol. 19 Issue 6, p593-615. 23p.
Subjects: Numerical analysis, Balanced truncation, Mathematical symmetry, Lyapunov functions, Iterative methods (Mathematics), Mathematical models
Abstract: We consider balanced truncation model order reduction for symmetric second-order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method. Stopping criteria for this iteration are investigated, and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal-oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical & Computer Modelling of Dynamical Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Benner%2C+Peter%22">Benner, Peter</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kürschner%2C+Patrick%22">Kürschner, Patrick</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kuerschner@mpi-magdeburg.mpg.de</i><br /><searchLink fieldCode="AR" term="%22Saak%2C+Jens%22">Saak, Jens</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+%26+Computer+Modelling+of+Dynamical+Systems%22">Mathematical & Computer Modelling of Dynamical Systems</searchLink>. Dec2013, Vol. 19 Issue 6, p593-615. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Balanced+truncation%22">Balanced truncation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+symmetry%22">Mathematical symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We consider balanced truncation model order reduction for symmetric second-order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method. Stopping criteria for this iteration are investigated, and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal-oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematical & Computer Modelling of Dynamical Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/13873954.2013.794363
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      – Code: eng
        Text: English
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        PageCount: 23
        StartPage: 593
    Subjects:
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Balanced truncation
        Type: general
      – SubjectFull: Mathematical symmetry
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Mathematical models
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      – TitleFull: An improved numerical method for balanced truncation for symmetric second-order systems.
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            – D: 01
              M: 12
              Text: Dec2013
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              Y: 2013
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