The Error Bound of Timing Domain in Model Order Reduction by Krylov Subspace Methods

In this paper, we present four different error bound estimates of timing domain in model order reduction by Krylov subspace methods. Firstly, we give integral method based on the impulse response in time domain. The second method is to use small sample statistical method to estimate the error bound based on an error system. The error induced by model order reduction process is constructed by an independent system output. We next present the error bound based on frequency domain error bound transformed into time domain method. The final method is reconstructing an error system, which is factorized to the sum of two parts, resulting from model order reduction by Krylov subspace. It is shown that the first factor is of the reduced order system except for subtracting an auxiliary variable, while the second factor is of the original system except for adding an auxiliary variable. In addition, we also give the analysis of the four methods. A few numerical examples are used to show the efficiency of the four different error bound estimate methods.