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Model Reduction and Approximation: Theory and Algorithms
Once the full models have been identified, a reduced model was created using a stepdown model reduction technique that identifies the best parsimonious model using the concordance index as a stopping criterion.
Model Reduction. Once the POD basis functions have been identified using the method of snapshots, the Euler equations must be recast to solve the modal coefficients in lieu of the full-system variables.
Many model reduction methods have been proposed in the last few decades, such as Krylov subspace model reduction methods [18,25], orthogonal polynomial model reduction methods [13,14,21], the proper orthogonal decomposition (POD) [10,17] and [H.sub.2] optimal model reduction methods [6,8].
The main topics of the conference were large-scale matrix equations, eigenvalue problems and preconditioning, ill-posed problems, model reduction methods, numerical methods for PDEs, and applications.
Further model reduction or optimization of CPU load and foor space is required to meet cylinder by cylinder NOx predictions.
Model reduction means to replace the given mathematical model (1) by a much smaller model which preserves certain crucial properties of the original model, such as stability and passivity, and it is then amenable for simulation and analysis.
The Introduction is organized differently and contains a paragraph addressing the issue of closed loop model reduction. There are more explanations and Figure 9 in Section 6, Controller Design.
Model reduction reduces the large system to a moderate size system, which has much less states and retains essential properties of the original system, so as to enable a fast numerical simulation [4, 5].
In order to overcome these issues, one solution is to perform model reduction. The use of appropriate reduction bases for the prediction of squeal frequencies and self-excited vibrations during the squeal event and its associated numerical implementation are complex tasks.
Keywords: Chemical kinetics, Chemical equilibrium, Lyapunov function, Invariant manifolds, Model reduction.

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