Moment Matching Theorems for Dimension Reduction of Higher-Order Dynamical Systems via Higher-Order Krylov Subspaces
نویسندگان
چکیده
Moment matching theorems for Krylov subspace based model reduction of higherorder linear dynamical systems are presented in the context of higher-order Krylov subspaces. We introduce the definition of a nth-order Krylov subspace Kn k ({Ai} n i=1;u) based on a sequence of n square matrices {Ai}i=1 and vector u. This subspace is a generalization of Krylov subspaces for higher-order systems, incorporating the standard Krylov subspace Kk(A;u) and the second-order Krylov subspace Gk(A,B;u) as special cases. Krylov subspace based structure preserving model reduction onto this subspace eliminates the linearization step of rewriting the higher-order system in an equivalent first-order form to prove moment-matching properties.
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