  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 (MIMO). This approach is based on the projection of the initial problem
onto tangential Krylov subspaces to produce a simpler reduced-order model that
approximates well the behavior of the original model. We present an algorithm
named: Adaptive Block Tangential Lanczos-type (ABTL) algorithm. We give some
algebraic properties and present some numerical experiences to show the
effectiveness of the proposed algorithms.
