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Showing 1 to 8 of 8 for “"IRKA"”.
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Iterative Rational Krylov Algorithm for Unstable Dynamical Systems and Genaralized Coprime Factorizations
… system. The Iterative Rational Krylov Algorithm (IRKA) is a robust model reduction technique which is used to locally reduce stable linear dynamical systems optimally in the ℋ₂-norm. While we cannot guarantee that IRKA reduces an unstable model optimally, there are no numerical obstacles to the …
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Finite Horizon Optimality and Operator Splitting in Model Reduction of Large-Scale Dynamical System
… the Iterative Rational Krylov Algorithm (IRKA), Balanced Truncation (BT), and Hankel Norm Approximation. However, these methods generally target stable systems and the approximation is performed over an infinite time horizon. If we are interested in a finite horizon reduced model, we …
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An Interpolation-Based Approach to Optimal H<sub>∞</sub> Model Reduction
… conditions can be computed iteratively using the IRKA algorithm [12]. We consider the special case of state-space symmetric systems and show that simple sufficient conditions can be derived for minimizing the approximation error when starting from the interpolation points found by the IRKA …
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Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs
… using the Iterative Rational Krylov Algorithm (IRKA), which iterates this Krylov reduction process to obtain an optimal ℋ₂ reduced model. This dissertation studies interpolatory model reduction for first-order descriptor systems, second-order systems, and DAEs. The main computational cost of …
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Inexact Solves in Interpolatory Model Reduction
… The Iterative Rational Krylov Algorithm (IRKA) iterates this Krylov reduction process to obtain an optimal Η₂ reduced model. Especially in the large-scale setting, these linear systems often require employing inexact solves. The aim of this thesis is to investigate the impact of inexact …
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Model Reduction of Power Networks
… Quadratic Iterative Rational Krylov Algorithm (Q-IRKA). Using a special subspace structure of the model reduction bases resulting from Q-IRKA and the structure of the underlying power network model, we form our final reduction basis that yields a reduced model of the same second-order structure as …
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Recycling Krylov Subspaces and Preconditioners
… BiCG in the Iterative Rational Krylov Algorithm (IRKA) for interpolatory model reduction and in the VMC algorithm. For a model reduction problem, we show up to 70% savings in iterations, and we also demonstrate that solving the problem without recycling leads to (about) a 50% increase in runtime. …
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Model Reduction of Nonlinear Fire Dynamics Models
Due to the complexity, multi-scale, and multi-physics nature of the mathematical models for fires, current numerical models require too much computational effort to be useful in design and real-time decision making, especially when dealing with fires over large domains. To reduce the computational …