Matrix Krylov subspace methods for linear systems with multiple right-hand sides |
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| Authors: | Email author" target="_blank">M?HeyouniEmail author A?Essai |
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| Institution: | 1.Laboratoire de Mathématiques Pures et Appliquées Joseph-Liouville,Université du Littoral C?te d'Opale,Calais Cedex,France;2.Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3,Université des Sciences et Technologies de Lille,Villeneuve d'Ascq Cedex,France |
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| Abstract: | In this paper, we first give a result which links any global Krylov method for solving linear systems with several right-hand
sides to the corresponding classical Krylov method. Then, we propose a general framework for matrix Krylov subspace methods
for linear systems with multiple right-hand sides. Our approach use global projection techniques, it is based on the Global
Generalized Hessenberg Process (GGHP) – which use the Frobenius scalar product and construct a basis of a matrix Krylov subspace
– and on the use of a Galerkin or a minimizing norm condition. To accelerate the convergence of global methods, we will introduce
weighted global methods. In these methods, the GGHP uses a different scalar product at each restart. Experimental results
are presented to show the good performances of the weighted global methods.
AMS subject classification 65F10 |
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| Keywords: | linear systems multiple right-hand sides matrix Krylov subspace weighted global Arnoldi and global Hessenberg processes matrix equations |
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