Model reduction via an LFT-based explicitly restarted nonsymmetric Lanczos algorithm

The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large scale systems of the form f(s) = c (sI−A)−1b, to exploit the sparse structure and reduce the computational burden. However, a good approximation is, usually, achieved only with relatively high order reduced models. Moreover, the computational cost of the Lanczos algorithm is dominated by the full rebiorthogonalization procedure, which is necessary because the Lanczos vectors tend to lose their biorthogonality. A method based on linear fractional transformations (LFTs) is proposed to compute a reduced mth order model by applying k “small” Lanczos algorithms with m/k steps each; thus reducing the computational cost and storage requirements. Applying this method, one can compute a tridiagonal similar realization of f(s) and when combined with conventional model reduction techniques, a minimal or reduced realization.