# A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

@article{Benner2015ASO,
title={A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems},
author={Peter Benner and Serkan Gugercin and Karen E. Willcox},
journal={SIAM Rev.},
year={2015},
volume={57},
pages={483-531}
}
• Published 1 November 2015
• Engineering
• SIAM Rev.
United States. Air Force Office of Scientific Research (Computational Mathematics Grant FA9550-12-1-0420)
1,045 Citations

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## References

SHOWING 1-10 OF 243 REFERENCES

### Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

• Mathematics, Physics
SIAM J. Sci. Comput.
• 2012
We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The...

### Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Methods

This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/20641

### Interpolation-Based H2-Model Reduction of Bilinear Control Systems

• Mathematics, Computer Science
SIAM J. Matrix Anal. Appl.
• 2012
The problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known ${\cal H}_2$-norm for linear systems is discussed.

### On the Fast Solving of Parabolic Boundary Control Problems

We present a multi-grid method for the solution of boundary control problems with quadratic cost functions, where the state is a solution of a parabolic initial-boundary value problem. The

### Partial realization of descriptor systems

• Computer Science, Mathematics
Syst. Control. Lett.
• 2006

### Stochastic Finite Elements: A Spectral Approach

• Physics
• 1990
Representation of stochastic processes stochastic finite element method - response representation stochastic finite element method - response statistics numerical examples.

### Model reduction methods based on Krylov subspaces

The main ideas of reduction-order modelling techniques based on Krylov subspaces are reviewed and some applications of reduced- order modelling in circuit simulation are described.

### Optimal interpolation-based model reduction

This dissertation is devoted to the development and study of new techniques in the field of model reduction for large-scale linear time-invariant (LTI) dynamical systems. The behavior of processes in