Journal of Global Optimization

, Volume 65, Issue 1, pp 19–32 | Cite as

A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations



In the present paper, we propose a preconditioned Newton–Block Arnoldi method for solving large continuous time algebraic Riccati equations. Such equations appear in control theory, model reduction, circuit simulation amongst other problems. At each step of the Newton process, we solve a large Lyapunov matrix equation with a low rank right hand side. These equations are solved by using the block Arnoldi process associated with a preconditioner based on the alternating direction implicit iteration method. We give some theoretical results and report numerical tests to show the effectiveness of the proposed approach.


ADI Block Arnoldi Block Krylov subspaces Low-rank approximations Lyapunov equation Newton Riccati Stein equation 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.L.M.P.AUniversité du LittoralCalais-CedexFrance
  2. 2.IUT Département de ChimieUniversité de Lille 1Villeneuve-d’AscqFrance

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