A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method

In this paper, we propose a new block Krylov-type subspace method for model reduction in large scale dynamical systems. We project the initial problem onto a new subspace, generated as a combination of rational and polynomial block Krylov subspaces. Simple algebraic properties are given and expressions of the error between the original and reduced transfer functions are established. Furthermore, we present an adaptive strategy of the interpolation points that will be used in the construction of our new block Krylov subspace. We also show how this method can be used to extract an approximate low rank solution of large-scale Lyapunov equations. Numerical results are reported on some benchmark examples to confirm the performance of our method compared with other known methods.

Automated summary

In this paper, a new block Krylov-type subspace method for model reduction in large scale dynamical systems is proposed. The method projects the initial problem onto a new subspace, generated as a combination of rational and polynomial block Krylov subspaces, and establishes expressions of the error between the original and reduced transfer functions. An adaptive strategy of the interpolation points is presented for constructing the new block Krylov subspace, and the method is shown to be effective in extracting approximate low rank solutions of large-scale Lyapunov equations. Numerical results on benchmark examples confirm the performance of the method compared to other known methods.