This article deals with the localization of eigenvalues of a large sparse and not necessarilysymmetric matrix in a domain of the complex plane. It combines two studies carried out earlier.The first work deals with the effect of applying small perturbations on a matrix, and referred to ase -spectrum or pseudospectrum. The second study describes a procedure for counting the numberof eigenvalues of a matrix in a region of the complex plain surrounded by a closed curve. The twomethods are combined in order to share the LU factorization of the resolvent, that intervenes in thetwo methods, so as to reduce the cost. The codes obtained are parallelized.