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In this paper, we present a new approach for model reduction of large scalefirst and second order dynamical systems with multiple inputs and multipleoutputs (MIMO). This approach is based on the projection of the initial problemonto tangential Krylov subspaces to produce a simpler reduced-order model thatapproximates well the behavior of the original model. We present an algorithmnamed: Adaptive Block Tangential Lanczos-type (ABTL) algorithm. We give somealgebraic properties and present some numerical experiences to show theeffectiveness of the proposed algorithms.

A block tangential Lanczos method for model reduction of large-scale first and second order dynamical systems