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The general Lanczos method and MIMO linear systems

The general Lanczos method (GLM) permits us to solve the breakdown and the block reduction problems related to the block version of the nonsymmetric Lanczos method. The main idea is to exploit the relation among Lanczos methods and Gram-Schmidt processes. The GLM generates the bases of two block Krylov subspaces, then MIMO control problems which can be formulated in terms of Krylov subspaces may be solved by using this method. In this paper, we show how it is possible to solve in this way, minimal realization and model reduction problems.