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The Global ETD Search service is a free service for researchers
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Showing 1 to 2 of 2 (0.046 seconds)Spelling suggestions: "subject:"smith method"" "subject:"amith method""
| 1 |
A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal controlPenzl, T. 30 October 1998 (has links) (PDF)
We present a new method for the computation of low rank approximations
to the solution of large, sparse, stable Lyapunov equations. It is based
on a generalization of the classical Smith method and profits by the
usual low rank property of the right hand side matrix.
The requirements of the method are moderate with respect to both
computational cost and memory.
Hence, it provides a possibility to tackle large scale control
problems.
Besides the efficient solution of the matrix equation itself,
a thorough integration of the method into several control
algorithms can improve their performance
to a high degree.
This is demonstrated for algorithms
for model reduction and optimal control.
Furthermore, we propose a heuristic for determining a set of
suboptimal ADI shift parameters. This heuristic, which is based on a
pair of Arnoldi processes, does not require any a priori
knowledge on the spectrum of
the coefficient matrix of the Lyapunov equation.
Numerical experiments show the efficiency of the iterative scheme
combined with the heuristic for the ADI parameters.
|
| 2 |
A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal controlPenzl, T. 30 October 1998 (has links)
We present a new method for the computation of low rank approximations
to the solution of large, sparse, stable Lyapunov equations. It is based
on a generalization of the classical Smith method and profits by the
usual low rank property of the right hand side matrix.
The requirements of the method are moderate with respect to both
computational cost and memory.
Hence, it provides a possibility to tackle large scale control
problems.
Besides the efficient solution of the matrix equation itself,
a thorough integration of the method into several control
algorithms can improve their performance
to a high degree.
This is demonstrated for algorithms
for model reduction and optimal control.
Furthermore, we propose a heuristic for determining a set of
suboptimal ADI shift parameters. This heuristic, which is based on a
pair of Arnoldi processes, does not require any a priori
knowledge on the spectrum of
the coefficient matrix of the Lyapunov equation.
Numerical experiments show the efficiency of the iterative scheme
combined with the heuristic for the ADI parameters.
|
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