h2-norm optimal model reduction for large scale discrete dynamical MIMO systems
Journal of Computational and Applied Mathematics
Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity
Automatica (Journal of IFAC)
Operation Stacking for Ensemble Computations With Variable Convergence
International Journal of High Performance Computing Applications
Model reduction for large-scale dynamical systems via equality constrained least squares
Journal of Computational and Applied Mathematics
A Framework for Reduced Order Modeling with Mixed Moment Matching and Peak Error Objectives
SIAM Journal on Scientific Computing
A note on shifted Hessenberg systems and frequency response computation
ACM Transactions on Mathematical Software (TOMS)
Original article: Machine tool simulation based on reduced order FE models
Mathematics and Computers in Simulation
$\mathcal{H}_2$-Optimal Model Reduction with Higher-Order Poles
SIAM Journal on Matrix Analysis and Applications
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
SIAM Journal on Numerical Analysis
Interpolatory Projection Methods for Parameterized Model Reduction
SIAM Journal on Scientific Computing
Model order reduction of coupled circuit-device systems
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
SIAM Journal on Numerical Analysis
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
Automatica (Journal of IFAC)
Mathematics and Computers in Simulation
On the ADI method for the Sylvester equation and the optimal-H2 points
Applied Numerical Mathematics
Identification of microwave filters by analytic and rational H2 approximation
Automatica (Journal of IFAC)
Structure-preserving model reduction of passive and quasi-active neurons
Journal of Computational Neuroscience
A shared memory parallel implementation of the IRKA algorithm for H2 model order reduction
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Interpolatory weighted-H2 model reduction
Automatica (Journal of IFAC)
Computational Optimization and Applications
Model reduction of linear time-varying systems over finite horizons
Applied Numerical Mathematics
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The optimal $\mathcal{H}_2$ model reduction problem is of great importance in the area of dynamical systems and simulation. In the literature, two independent frameworks have evolved focusing 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 paper, we develop a new unifying framework for the optimal $\mathcal{H}_2$ approximation problem using best approximation properties in the underlying Hilbert space. This new framework leads to a new set of local optimality conditions taking the form of a structured orthogonality condition. We show that the existing Lyapunov- and interpolation-based conditions are each equivalent to our conditions and so are equivalent to each other. Also, we provide a new elementary proof of the interpolation-based condition that clarifies the importance of the mirror images of the reduced system poles. Based on the interpolation framework, we describe an iteratively corrected rational Krylov algorithm for $\mathcal{H}_2$ model reduction. The formulation is based on finding a reduced order model that satisfies interpolation-based first-order necessary conditions for $\cHtwo$ optimality and results in a method that is numerically effective and suited for large-scale problems. We illustrate the performance of the method with a variety of numerical experiments and comparisons with existing methods.