A deflated implicitly restarted Lanczos algorithm for model reduction

The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large-scale systems to exploit the sparse structure and reduce the computational burden. An implicit restart scheme for the standard nonsymmetric Lanczos algorithm is developed in this paper, based on the deflation of the non-minimal part of the reduced-order model. The deflation is achieved by balanced truncation, and using a modified A matrix at each iteration prevents discarded information from reappearing in the projected model after restarting. The main advantage is that the interesting information from the Krylov subspaces is compressed into a pair of fixed-size Krylov bases.