In this paper, we focus on structure-preserving model order reduction (SPMOR) of the second-order system using the Iterative Rational Krylov Algorithm (IRKA). In general, the standard IRKA can be used to the second-order structure system by converting the system into an equivalent first-order form  . In this case, the reduced model can not preserve the structure of the second-order form which is however necessary for further manipulation. Here we develop IRKA based algorithm which enables us to generate a reduced second-order system without explicitly converting the system into a first-order form. A challenging task in IRKA is to select a set of better interpolation points and the tangential directions . To overcome these problems, this paper discusses how to select a set of good interpolation points and the tangential directions by an internal formulation. Also, this paper talks out the \mathcal{H system. The theoretical results are experimented by applying them to several sets of data of large-scale dynamical systems. Numerical results are discussed to show the applicability and efficiency of the proposed techniques .
In this paper, we focus on the efficient techniques to estimate the \mathcal{H (SPMOR) of the second-order systems using the Iterative Rational Krylov Algorithm (IRKA). In general, the classical IRKA can be applied to the second-order system by converting it into an equivalent first-order form and get the reduced model in a first-order form . In this case, the reduced model can not preserve the structure of the second-order system which is however necessary for further manipulation. Here we develop IRKA based algorithms that enable us to generate approximate reduced second-order systems without explicitly converting the systems into a first-order form. On the other hand, there are very challenging tasks to find reduced-order form of a large-scale system with a minimized \mathcal{H . To overcome these problems, this paper discusses competent techniques to determine the optimal \mathcal{H system. The efficiency and applicability of the proposed techniques are validated by applying them to several large-scale dynamical systems. The computation is done numerically and the achieved results are discussed in both tabular and graphical approaches .
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structure-preserving model order reduction
the efficient techniques to estimate the \mathcal{H
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system
systems
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standard
classical
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used
applied
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structure
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the system
it
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and get the reduced model in a first-order form
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form
system
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algorithm which enables
algorithms that enable
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approximate
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system
systems
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system
systems
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A challenging task in IRKA is to select a set of better interpolation points and the tangential directions
On the other hand, there are very challenging tasks to find reduced-order form of a large-scale system with a minimized \mathcal{H
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how to select a set of good interpolation points and the tangential directions by an internal formulation. Also, this paper talks out the \mathcal{H
competent techniques to determine the optimal \mathcal{H
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theoretical results are experimented
efficiency and applicability of the proposed techniques are validated
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sets of data of
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Numerical
The computation is done numerically and the achieved
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to show the applicability and efficiency of the proposed techniques
in both tabular and graphical approaches