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On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations

1
Laboratory LAMAI, University of Cadi Ayyad, Marrakesh 40000, Morocco
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LMPA, 50 rue F. Buisson, ULCO Calais, Calais 62228 , France
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ENSA d’EL Jadida, University Chouaib Doukkali, EL Jadida 24002, Morocco
*
Author to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Mathematics 2017, 5(2), 21; https://doi.org/10.3390/math5020021
Received: 22 December 2016 / Revised: 15 March 2017 / Accepted: 17 March 2017 / Published: 27 March 2017
(This article belongs to the Special Issue Numerical Linear Algebra with Applications)
In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA) or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments. View Full-Text
Keywords: extended block Krylov subspaces; low-rank approximation; Stein matrix equation; Galerkin approach (GA); minimal residual (MR) methods extended block Krylov subspaces; low-rank approximation; Stein matrix equation; Galerkin approach (GA); minimal residual (MR) methods
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MDPI and ACS Style

Bentbib, A.H.; Jbilou, K.; Sadek, E.M. On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations. Mathematics 2017, 5, 21. https://doi.org/10.3390/math5020021

AMA Style

Bentbib AH, Jbilou K, Sadek EM. On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations. Mathematics. 2017; 5(2):21. https://doi.org/10.3390/math5020021

Chicago/Turabian Style

Bentbib, Abdeslem H.; Jbilou, Khalide; Sadek, EL M. 2017. "On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations" Mathematics 5, no. 2: 21. https://doi.org/10.3390/math5020021

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