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- Serkan Gugercin, Athanasios C. Antoulas, Christopher A. Beattie
- SIAM J. Matrix Analysis Applications
- 2008

The optimal H 2 model reduction problem is of great importance in the area of dynamical systems and simulation. In the literature, two independent frameworks have evolved focussing either on solution of Lyapunov equations on the one hand or interpolation of transfer functions on the other, without any apparent connection between the two approaches. In this… (More)

- Christopher A. Beattie, Mark Embree, John Rossi
- SIAM J. Matrix Analysis Applications
- 2004

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of… (More)

- Ulrike Baur, Christopher A. Beattie, Peter Benner, Serkan Gugercin
- SIAM J. Scientific Computing
- 2011

We provide a unifying projection-based framework for structure-preserving interpo-latory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model.… (More)

- Christopher A. Beattie, Mark Embree, Danny C. Sorensen
- SIAM Review
- 2005

Krylov subspace methods have proved effective for many non-Hermitian eigenvalue problems, yet the analysis of such algorithms is involved. Convergence can be characterized by the angle the approximating subspace forms with a desired invariant subspace, resulting in a geometric framework that is robust to eigenvalue ill-conditioning. This paper describes a… (More)

— 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 the model-to-be-reduced. In this paper, by exploiting the Loewner-matrix approach for interpolation, we develop a new formulation of IRKA that only requires… (More)

- Christopher A. Beattie
- Math. Comput.
- 2000

How close are Galerkin eigenvectors to the best approximation available out of the trial subspace ? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace – and this occurs more rapidly than the underlying rate of convergence of the… (More)

- Christopher A. Beattie, Serkan Gugercin
- ArXiv
- 2014

The last two decades have seen major developments in inter-polatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined methods for deriving inter-polatory reduced models directly from input/output measurements; and extensions for the… (More)

Large-scale simulations play a crucial role in the study of a great variety of complex physical phenomena, leading often to overwhelming demands on computational resources. Managing these demands constitutes the main motivation for model reduction: produce simpler reduced-order models (which allow for faster and cheaper simulation) while accurately… (More)

- Christopher A. Beattie, Serkan Gugercin
- Systems & Control Letters
- 2009

We present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization C(s) (s) −1 B(s) + D. This includes rational Krylov-based interpolation methods as a special case. The broader framework allows retention of special structure in reduced models such as symmetry, second-and higher order structure, state… (More)