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Mathematics 2017, 5(2), 21; doi:10.3390/math5020021

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

1
Laboratory LAMAI, University of Cadi Ayyad, Marrakesh 40000, Morocco
2
LMPA, 50 rue F. Buisson, ULCO Calais, Calais 62228 , France
3
ENSA d’EL Jadida, University Chouaib Doukkali, EL Jadida 24002, Morocco
*
Author to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
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)
View Full-Text   |   Download PDF [314 KB, uploaded 28 March 2017]   |  

Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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.

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