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The main goal of this work is solving system of linear equations Ax = b, where A is a n_n square matrix, b is a n_1 vector and x is the vector of unknowns. When n is large, using direct methods is not economical. Thus, the system is solved by iterative methods. At first, projection method onto subspace K _ Rn with dimension m _ n is described, and then this subspace K is equalized with the krylov subspace. Then,some samples of projection methods onto the krylov subspace, such as FOM, GMRES and CG (Conjugate Gradient), are considered. The preconditioning of the linear system is explained, that is, instead of solving system Ax = b, the system PAx = Pb (P nonsingular), is solved, such that the... 

In this essay we study the concepts of nuclearity in C-algebras, and amenability in Banach algebras. A proof on the "every amenable C-algebra is nuclear" is studied. A Banach algebra A is called amenable if every continous derivation D : A ! E , is inner i.e. there exists anif in this denition E is a dual Banach A-module and norm continuity replace by w-continuity then we have Connes-amenability; Connes-amenability was rst considered for von Neumann algebras in [J-K-R] (and thus should perhaps be called Johnson-Kadison-Ringrose amenability). The reason why this notion of amenability is usually associated with A. Connes are his papers [Conn 1] and [Conn 2] The name "Connes-amenability" seems... 

Farctional Brownian motion (fBm) is a Gaussian Stochastic process B={B_t ∶t ≥0} With zero mean and Covariance function given by RH (t,s)=1/2 (t^2H+ S^2H-├|t-├ s┤|┤ 〖^2H〗) Where 0