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

The optimal H2 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 interpolatory 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)

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)

In this note, we examine Krylov-based model reduction of second order systems where proportional damping is used to model energy dissipation. We give a detailed analysis of the distribution of system poles, and then, through a connection with potential theory, we are able to exploit the structure of these poles to obtain an optimal single shift strategy… (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)

Mathematics (ABSTRACT) This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush–Kuhn–Tucker (KKT) optimality conditions or in interior–point methods. Therefore, the system matrix is… (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)

- 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)−1B(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, secondand higher order structure, state… (More)