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.

在本文中，我们提出了一种新的块Krylov型子空间方法，用于大规模动力学系统的模型约简。我们将初始问题投影到一个新的子空间上，该子空间是由有理块和多项式块Krylov子空间的组合生成的。给出了简单的代数性质，并建立了原始传递函数和简化传递函数之间的误差表达式。此外，我们提出了一种插值点的自适应策略，该策略将用于构造新的块Krylov子空间。我们还展示了如何使用此方法来提取大规模Lyapunov方程的近似低秩解。在一些基准示例上报告了数值结果，以证实我们的方法与其他已知方法相比的性能。