# Stability Analysis of Inexact Solves in Moment Matching based Model Reduction

@article{Singh2018StabilityAO, title={Stability Analysis of Inexact Solves in Moment Matching based Model Reduction}, author={Navneet Pratap Singh and Kapil Ahuja}, journal={ArXiv}, year={2018}, volume={abs/1803.09283} }

Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm (Bonin et. al., 2016), has been proposed. The main computational cost of the AIRGA algorithm is solving a sequence of linear systems. Usually, direct methods (e.g., LU) are used for solving these systems. As model sizes grow, direct methods become prohibitively expensive. Iterative methods (e.g., Krylov) scale well with…

## 2 Citations

Inexact Linear Solves in Model Reduction of Bilinear Dynamical Systems

- Computer ScienceIEEE Access
- 2019

The stability analysis techniques that are proposed here can be extended to many other methods for doing the MOR of bilinear dynamical systems, e.g., using balanced truncation or the ADI methods.

ℋ2 sub-optimal model reduction for second-order network systems

- Mathematics, Computer Science2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This paper studies a moment matching model reduction method for second-order network systems that achieves moment matching and shows the effectiveness of the proposed method.

## References

SHOWING 1-10 OF 28 REFERENCES

Large‐scale topology optimization using preconditioned Krylov subspace methods with recycling

- Computer Science, Mathematics
- 2007

It is shown that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density.

A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching

- Computer Science
- 2014

This work proposes a numerically stable algorithm for PMOR based on multi-moment matching that generates a projection matrix for model reduction by implicit moment matching.

Approximate Inverse Preconditioners via Sparse-Sparse Iterations

- Computer ScienceSIAM J. Sci. Comput.
- 1998

Newton, "global," and column-oriented algorithms, and options for initial guesses, self-preconditioning, and dropping strategies are discussed, and some limited theoretical results on the properties and convergence of approximate inverses are derived.

Recycling BiCGSTAB with an Application to Parametric Model Order Reduction

- Computer ScienceSIAM J. Sci. Comput.
- 2015

This work modifications the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate invariant subspaces, and extends this recycling theory to Bi CGSTAB.

A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping

- Computer ScienceMath. Comput. Simul.
- 2016

Global FOM and GMRES algorithms for matrix equations

- Mathematics, Computer Science
- 1999

Recycling Krylov Subspaces for Sequences of Linear Systems

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2006

This work proposes and analyzes two methods that significantly reduce the total number of matrix-vector products required to solve all systems and can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems.

Recycling BiCG with an Application to Model Reduction

- Computer ScienceSIAM J. Sci. Comput.
- 2012

Rec recycling BiCG is introduced, a BiCG method that recycles two Krylov subspaces from one pair of dual linear systems to the next pair and builds the foundation for developing recycling variants of other bi-Lanczos based methods, such as CGS, BiCGSTAB, QMR, and TFQMR.