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Approximation of large-scale dynamical systems: an overview

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Antoulas A. C., Sorensen D. C.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 5
1093-1121
EN
In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.
2
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Efficient numerical algorithms for balanced stochastic truncation

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Benner P., Quintana-Ortí E. S., Quintana-Ortí G.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 5
1123-1150
EN
We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation of balanced stochastic truncation model reduction.
3
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Reduction of large circuit models via low rank approximate gramians

100%
Li J.-R., White J.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 5
1151-1171
EN
We describe a model reduction algorithm which is well-suited for the reduction of large linear interconnect models. It is an orthogonal projection method which takes as the projection space the sum of the approximate dominant controllable subspace and the approximate dominant observable subspace. These approximate dominant subspaces are obtained using the Cholesky Factor ADI (CF-ADI) algorithm. We describe an improvement upon the existing implementation of CF-ADI which can result in significant savings in computational cost. We show that the new model reduction method matches moments at the negative of the CF-ADI parameters, and that it can be easily adapted to allow for DC matching, as well as for passivity preservation for multi-port RLC circuit models which come from modified nodal analysis.
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