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

Abdeslem Hafid Bentbib, Khalide Jbilou and Mostafa Sadek El
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Abdeslem Hafid Bentbib: Laboratory LAMAI, University of Cadi Ayyad, Marrakesh 40000, Morocco
Khalide Jbilou: LMPA, 50 rue F. Buisson, ULCO Calais, Calais 62228 , France
Mostafa Sadek El: ENSA d’EL Jadida, University Chouaib Doukkali, EL Jadida 24002, Morocco

Mathematics, 2017, vol. 5, issue 2, 1-13

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.

Keywords: extended block Krylov subspaces; low-rank approximation; Stein matrix equation; Galerkin approach (GA); minimal residual (MR) methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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