Block Arnoldi-based methods for large scale discrete-time algebraic Riccati equations

Authors:
A. Bouhamidi;M. Heyouni;K. Jbilou
Affiliations:
Univ. Lille- Nord de France, ULCO, LMPA, 50 rue F. Buisson BP699, F-62228 Calais Cedex, France;ENSAH, Ecole Nationale des Sciences Appliquées d'Al-Hoceima, Université Mohammed Premier, Oujda, Maroc;Univ. Lille- Nord de France, ULCO, LMPA, 50 rue F. Buisson BP699, F-62228 Calais Cedex, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In the present paper, we present block Arnoldi-based methods for the computation of low rank approximate solutions of large discrete-time algebraic Riccati equations (DARE). The proposed methods are projection methods onto block or extended block Krylov subspaces. We give new upper bounds for the norm of the error obtained by applying these block Arnoldi-based processes. We also introduce the Newton method combined with the block Arnoldi algorithm and present some numerical experiments with comparisons between these methods.