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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)

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)

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)

- Astrid Battermann, Matthias Heinkenschloss, Christopher Beattie, John A Burns
- 1996

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)

— 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)

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)

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)

— We present a trust-region approach for optimal H2 model reduction of multiple-input/multiple-output (MIMO) linear dynamical systems. The proposed approach generates a sequence of reduced order models producing monotone improving H2 error norms and is globally convergent to a reduced order model guaranteed to satisfy first-order optimality conditions with… (More)

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)

— Port network modeling of physical systems leads directly to an important class of passive state space systems: port-Hamiltonian systems. We consider here methods for model reduction of large scale port-Hamiltonian systems that preserve port-Hamiltonian structure and are capable of yielding reduced order models that satisfy first-order optimality… (More)