# A Rational Krylov Iteration for Optimal H 2 Model Reduction

@inproceedings{Gugercin2006ARK, title={A Rational Krylov Iteration for Optimal H 2 Model Reduction}, author={Serkan Gugercin and Athanasios C. Antoulas and Christopher A. Beattie}, year={2006} }

In the sequel, we will construct the reduced order models Gr(s) through Krylov projection methods. Toward this end, we construct matrices V ∈ R and Z ∈ R that span certain Krylov subspaces with the property that Z V = Ir. The reduced order model Gr(s) will then be obtained as Ar = Z T AV, Br = Z T B, and Cr = CV. (2) The corresponding oblique projection is given by V Z . Many researchers have worked on the problem (1); see [18], [16], [7], [5], [3], [17], [4] and references therein. Since…

## 47 Citations

Realization-independent H 2-approximation

- 2012

Iterative Rational Krylov Algorithm (IRKA) of [11] is an effective tool for tackling the H2-optimal model reduction problem. However, so far it has relied on a first-order state-space realization of…

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- Mathematics, Computer Science2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
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A Loewner-matrix approach for interpolation is employed, and a new formulation of IRKA is developed that only uses transfer function evaluations, without requiring any particular realization, to be extended to H2 approximation of irrational, infinite-dimensional dynamical systems.

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- Mathematics, Computer Science2010 Sixth International Conference on Natural Computation
- 2010

A new SVD-Krylov based method is proposed, which is equivalent to compute an equality constrained least-squares problem and is numerically effective and suited for large-scale problem, which can be verified in the numerical examples.

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This paper is concerned with the construction of reduced–order models for high–order linear systems in such a way that the L2 norm of the impulse–response error is minimized. Two convergent…

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- 2016

Numerical solution of dynamical systems have been a successful means for studying complex physical phenomena. However, in large-scale setting, the system dimension makes the computations infeasible…

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Summary. We compare different model reduction methods applied to the dynamical system of a coupled transmission line: balanced truncation (BT), truncation by balancing one gramian (or PMTBR - poor…

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- Computer Science, MathematicsSIAM J. Sci. Comput.
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