Two-step Lanczos algorithm for model order reduction

The Pade-Via-Lanczos (PVL) algorithm proved to be a reliable technique for obtaining reduced-order models of electromagnetic devices. Its computational complexity is, however, quite large, since it involves inversion or factorization of a matrix which can be, for complex devices, on the order of hundreds of thousands. The present paper proposes a two-step approach based entirely on the Lanczos algorithm, meant to drastically reduce the computational complexity. In the first step, a Lanczos-based projection technique is used to reduce the un-inverted matrix to a manageable size, which can be dealt with by the PVL method in the second step. The computing time was thus reduced by a factor of ten, as compared to the classical PVL.