, 55:13 | Cite as

An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems

  • H. Barkouki
  • A. H. Bentbib
  • M. Heyouni
  • K. Jbilou


In this paper, we propose an extended block Krylov process to construct two biorthogonal bases for the extended Krylov subspaces \(\mathbb {K}_{m}^e(A,V)\) and \(\mathbb {K}_{m}^e(A^{T},W)\), where \(A \in \mathbb {R}^{n \times n}\) and \(V,~W \in \mathbb {R}^{n \times p}\). After deriving some new theoretical results and algebraic properties, we apply the proposed algorithm with moment matching techniques for model reduction in large scale dynamical systems. Numerical experiments for large and sparse problems are given to show the efficiency of the proposed method.


Extended block Lanczos algorithm Model-order reduction Moment matching Transfer function 

Mathematics Subject Classification

65F 15A 



We would like to thank the referees for valuable remarks and helpful suggestions.


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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  • H. Barkouki
    • 1
  • A. H. Bentbib
    • 1
    • 2
  • M. Heyouni
    • 3
  • K. Jbilou
    • 2
  1. 1.Faculté des Sciences et Techniques-GuelizLaboratoire de Mathématiques Appliquées et InformatiqueMarrakechMorocco
  2. 2.Université du LittoralCalais CedexFrance
  3. 3.ENSA, Equipe EMMA, Laboratoire LSIAUniversité Mohammed PremierOujdaMorocco

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