## Krylov Subspace Techniques for Reduced-Order Modeling of Nonlinear Dynamical Systems (2002)

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Venue: | Appl. Numer. Math |

Citations: | 50 - 3 self |

### BibTeX

@ARTICLE{Bai02krylovsubspace,

author = {Zhaojun Bai and Daniel Skoogh},

title = {Krylov Subspace Techniques for Reduced-Order Modeling of Nonlinear Dynamical Systems},

journal = {Appl. Numer. Math},

year = {2002},

volume = {43},

pages = {9--44}

}

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### Abstract

Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of large-scale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bi-linearization method, which extends Krylov subspace techniques for linear systems. In this approach, the nonlinear system is first approximated by a bilinear system through Carleman bilinearization. Then a reduced-order bilinear system is constructed in such a way that it matches certain number of multimoments corresponding to the first few kernels of the Volterra-Wiener representation of the bilinear system. It is shown that the two-sided Krylov subspace technique matches significant more number of multimoments than the corresponding one-side technique.