Spelling suggestions: "subject:"generalized lyapunov equations"" "subject:"generalized yapunov equations""
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Balanced Truncation Model Reduction of Large and Sparse Generalized Linear SystemsBadía, José M., Benner, Peter, Mayo, Rafael, Quintana-Ortí, Enrique S., Quintana-Ortí, Gregorio, Remón, Alfredo 26 November 2007 (has links) (PDF)
We investigate model reduction of large-scale linear time-invariant systems in
generalized state-space form. We consider sparse state matrix pencils, including
pencils with banded structure. The balancing-based methods employed here are
composed of well-known linear algebra operations and have been recently shown to be
applicable to large models by exploiting the structure of the matrices defining
the dynamics of the system.
In this paper we propose a modification of the LR-ADI iteration to solve
large-scale generalized Lyapunov equations together with a practical
convergence criterion, and several other implementation refinements.
Using kernels from several serial and parallel linear algebra libraries,
we have developed a parallel package for model reduction, SpaRed, extending
the applicability of balanced truncation to sparse systems with up to
$O(10^5)$ states.
Experiments on an SMP parallel architecture consisting of Intel Itanium 2 processors
illustrate the numerical performance of this approach and the potential of the
parallel algorithms for model reduction of large-scale sparse systems.
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Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel ProfilesBadía, José M., Benner, Peter, Mayo, Rafael, Quintana-Ortí, Enrique S., Quintana-Ortí, Gregorio, Saak, Jens 06 September 2006 (has links) (PDF)
We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.
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Balanced Truncation Model Reduction of Large and Sparse Generalized Linear SystemsBadía, José M., Benner, Peter, Mayo, Rafael, Quintana-Ortí, Enrique S., Quintana-Ortí, Gregorio, Remón, Alfredo 26 November 2007 (has links)
We investigate model reduction of large-scale linear time-invariant systems in
generalized state-space form. We consider sparse state matrix pencils, including
pencils with banded structure. The balancing-based methods employed here are
composed of well-known linear algebra operations and have been recently shown to be
applicable to large models by exploiting the structure of the matrices defining
the dynamics of the system.
In this paper we propose a modification of the LR-ADI iteration to solve
large-scale generalized Lyapunov equations together with a practical
convergence criterion, and several other implementation refinements.
Using kernels from several serial and parallel linear algebra libraries,
we have developed a parallel package for model reduction, SpaRed, extending
the applicability of balanced truncation to sparse systems with up to
$O(10^5)$ states.
Experiments on an SMP parallel architecture consisting of Intel Itanium 2 processors
illustrate the numerical performance of this approach and the potential of the
parallel algorithms for model reduction of large-scale sparse systems.
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Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel ProfilesBadía, José M., Benner, Peter, Mayo, Rafael, Quintana-Ortí, Enrique S., Quintana-Ortí, Gregorio, Saak, Jens 06 September 2006 (has links)
We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.
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