A tangential method for the balanced truncation in model reduction
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In this paper, we present a new approach for large-scale Lyapunov matrix equations, where we present two algorithms named: Adaptive Block Tangential Lanczos-type and Arnoldi-type algorithms (ABTL and ABTA). This approach is based on the projection of the initial problem onto tangential Krylov subspaces to produce a low-rank approximate solution of large Lyapunov equations. These approximations are used in model reduction of large-scale dynamical systems with multiple inputs and multiple outputs (MIMO). We give some algebraic properties and present some numerical experiences to show the effectiveness of the proposed algorithms.
KeywordsBalanced truncation Krylov subspaces Lyapunov Model reduction Tangential directions
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