# Approximation of Large-Scale Dynamical Systems

@inproceedings{Antoulas2005ApproximationOL, title={Approximation of Large-Scale Dynamical Systems}, author={Athanasios C. Antoulas}, booktitle={Advances in Design and Control}, year={2005} }

Preface Part I. Introduction: 1. Introduction 2. Motivating examples Part II. Preliminaries: 3. Tools from matrix theory 4. Linear dynamical systems, Part 1 5. Linear dynamical systems, Part 2 6. Sylvester and Lyapunov equations Part III. SVD-based Approximation Methods: 7. Balancing and balanced approximations 8. Hankel-norm approximation 9. Special topics in SVD-based approximation methods Part IV. Krylov-based Approximation Methods: 10. Eigenvalue computations 11. Model reduction using…

## 2,831 Citations

### An overview of approximation methods for large-scale dynamical systems

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### Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems

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- 2018

In this paper, we consider the balanced truncation method for model reductions in large-scale linear and time-independent dynamical systems with multi-inputs and multi-outputs. The method is based on…

### Second order H2 optimal approximation of linear dynamical systems

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- 2011

Abstract In this paper we consider the H 2 optimal model reduction problem which has important applications in system approximation and has received considerable attention in the literature. An…

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### Second order H 2 optimal approximation of linear dynamical systems

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- 2011

In this paper we consider the H2 optimal model reduction problem which has important applications in system approximation and has received considerable attention in the literature. An important link…

### Hankel-norm approximation of large-scale descriptor systems

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- 2020

The computation of the optimal Hankel-norm approximation is generalized to the case of linear time-invariant continuous-time descriptor systems and a new algebraic characterization of all-pass descriptor systems is developed and used to construct an efficient algorithm.

### Theoretical and practical aspects of linear and nonlinear model order reduction techniques

- Computer Science
- 2008

The effectiveness of the modified AISIAD method in generating a low order models that correctly describe the dispersion of the marker in the linear case is demonstrated and several methods for nonlinear model reduction when the diffusion and mobility constants become concentration-dependent are described.

### Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation

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### Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations

- Computer Science, MathematicsSIAM J. Numer. Anal.
- 2009

This paper analyzes the convergence of projection-type methods for approximating the solution matrix of large-scale continuous-time Lyapunov matrix equations and provides new asymptotic estimates for the error matrix under suitable hypotheses on the coefficient matrix.

### AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

- Computer ScienceThe ANZIAM Journal
- 2017

A new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach, an extension of the SVD-rational Krylov method.