Arnoldi-based model order reduction for linear systems with inhomogeneous initial conditions

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In this paper, we discuss the Arnoldi-based model order reduction (MOR) methods for linear systems with inhomogeneous initial conditions, and present a time domain MOR method by general orthogonal polynomials. The basic procedure is to use the expansion coefficient matrix in the orthogonal polynomial space satisfying a simple recurrence formula to generate a projection matrix, which is produced by a modified Arnoldi algorithm. Then, the resulting reduced model matches a desired number of the expansion coefficients of the original system. The approximate error estimate of the reduced model is given. Since the initial conditions are well represented by the subspaces constructed by our algorithm, it can well deal with those systems with inhomogeneous initial conditions. Two benchmark examples in real applications are simulated to illustrate the effectiveness of the proposed method.