The numerical solution of weakly singular integral equation gives rise to linear systems by using fractional wavelet bases as the projection method that can be rather challenging for iterative methods. In this paper we compare a number of new standard preconditioned approaches to solve some of these equations. We propose a family of accelerators of GMRES(m), combined with a few threshold based preconditioners such as ILUT(p, 0 ) on a number of linear systems arising from various integral

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... ns. Finally, we investigate the convergence of precondition effectively in linear system and function spaces. The results confirm that the precondititioning strategy for accelerating the convergence of the Krylov subspace method is effective. Mathematics Subject Classification: 65F36, 65N22, 65N38