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Abstract
The purpose of this paper is to acquire model reductions of large-scale quadratic dynamical systems. The idea for solving the problem is based on the relation between a quadratic system and its related enlarged linear system. That is, we transfer the second-order system to an enlarged first-order systems and obtain the second-order model reduction by converting the first-order model reduction to a second-order one. Next, we give a brief introduction for numerical methods of the first-order model reduction. Particularly, these methods can be categorized to two groups: (a) SVD based methods; (b)Krylov based methods. Finally, some numerical experiments are performed. The results of numerical implementation show that some serious round-off errors may occur when the first-order model reduction converts to the second-order one.
So, we conclude that the propose methods in this paper are eventually not good enough for the second-order reduction. However, a reliable and ecient method for the model reduction of a quadratic dynamical system is still under investigation.

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