Sylvester equations and projection-based model reduction
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method
SIAM Journal on Scientific Computing
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Brief paper: Krylov projection framework for Fourier model reduction
Automatica (Journal of IFAC)
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
SIAM Journal on Scientific Computing
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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In this paper, we present a new method of model reduction for large-scale dynamical systems, which belongs to the SVD-Krylov based method category. It is a two-sided projection where one side reflects the Krylov part and the other side reflects the SVD (observability gramian) part. The reduced model matches the first r+i Markov parameters of the full order model, and the remaining ones approximate in a least squares sense without being explicitly computed, where r is the order of the reduced system, and i is a nonnegative integer such that 1@?i