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Balanced truncation model reduction for linear time-varying systems.

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Title: Balanced truncation model reduction for linear time-varying systems.
Authors: Lang, N.1 (AUTHOR) norman.lang@mathematik.tu-chemnitz.de, Saak, J.1,2 (AUTHOR), Stykel, T.3 (AUTHOR)
Source: Mathematical & Computer Modelling of Dynamical Systems. Jul2016, Vol. 22 Issue 4, p267-281. 15p.
Subjects: Balanced truncation, Time integration scheme, Nonlinear integral equations, Square root, Factorization, Quantum mechanics
Abstract: A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high-order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort in treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied. [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="%22Lang%2C+N%2E%22">Lang, N.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> norman.lang@mathematik.tu-chemnitz.de</i><br /><searchLink fieldCode="AR" term="%22Saak%2C+J%2E%22">Saak, J.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Stykel%2C+T%2E%22">Stykel, T.</searchLink><relatesTo>3</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>. Jul2016, Vol. 22 Issue 4, p267-281. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Balanced+truncation%22">Balanced truncation</searchLink><br /><searchLink fieldCode="DE" term="%22Time+integration+scheme%22">Time integration scheme</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+integral+equations%22">Nonlinear integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Square+root%22">Square root</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+mechanics%22">Quantum mechanics</searchLink>
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  Label: Abstract
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  Data: A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high-order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort in treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied. [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: 10.1080/13873954.2016.1198386
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      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 267
    Subjects:
      – SubjectFull: Balanced truncation
        Type: general
      – SubjectFull: Time integration scheme
        Type: general
      – SubjectFull: Nonlinear integral equations
        Type: general
      – SubjectFull: Square root
        Type: general
      – SubjectFull: Factorization
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      – SubjectFull: Quantum mechanics
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              Text: Jul2016
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