A Tangential Block Lanczos Method for Model Reduction of Large-Scale First and Second Order Dynamical Systems

In this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs. This approach is based on the projection of the initial problem onto tangential subspaces to produce a simpler reduced-order model that approximates well the behaviour of the original model. We present an algorithm named: adaptive block tangential Lanczos-type algorithm. We give some algebraic properties and present some numerical experiences to show the effectiveness of the proposed algorithms.