论文标题
基于Gramian的模型订单减少与力矩匹配之间的联系
A link between gramian based model order reduction and moment matching
论文作者
论文摘要
我们分析了一个基于runge-kutta的家族，用于近似线性时间不变动态系统的近似值。近似的Gramians用于获得类似于平衡POD中使用的方法的近似平衡转换。结果表明，在此进行有理插值，因为大约跨越某些Krylov子空间。膨胀点主要取决于屠夫tableaus给出的时间步长和矩阵的特征值。
We analyze a family of Runge-Kutta based quadrature algorithms for the approximation of the gramians of linear time invariant dynamical systems. The approximated gramians are used to obtain an approximate balancing transformation similar to the approach used in balanced POD. It is shown that hereby rational interpolation is performed, as the approximants span certain Krylov subspaces. The expansion points are mainly determined by the time step sizes and the eigenvalues of the matrices given by the Butcher tableaus.
