The most successful iterative methods currently available are those based on the Krylov subspace which consists in forming a basis of a sequence of successive matrix powers times the initial residual. These methods are based on orthogonality of vectors of the Krylov subspace basis to solve generalized linear systems. The most well-known iterative Krylov subspace methods are Conjugate Gradient method and GMRES method (generalized minimal residual).
-%les chercheurs ont développer différentes méthodes exemple de méthode iteratives stationnaires et non stationnaires (krylov)
-%problème de convergence et difficulté dans le passage à l'échelle
+However, the iterative methods suffer from scalability problems on parallel computing platforms with many processors due to their need for reduction operations and collective communications to perform matrix-vector multiplications.
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