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Abstract
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In this thesis, we compared several iterative methods with each other. Here, we presented two new methods called WFOM and WGMRES, which are variants of FOM and GMRES, for solving large and sparse non symmetric linear systems. To accelerate the convergence, these new methods use a different inner products instead of the Euclidean one. Furthermore, at each restart, a different inner product is chosen. The Weighted-Arnoldi process is introduced for implementing these methods. After describing the Weighted methods, we give the relations that link them to FOM and GMRES. Experimental results are presented to show the good performances of the new methods compared to FOM(m) and GMRES(m). Then we discuss the preformance of the preconditioned WFOM and WGMRES. Numerical results are presented to show that, contrast to WFOM and WGMRES, the preconditioned WFOM and WGMRES have no good performance compared to preconditioned FOM(m) and preconditioned GMRES(m).
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