In this talk, we discuss the problem of computing eigenvalues and eigenvectors of a heterogeneous material or domain, and the numerical schemes to approximate them. We propose an improvement over the traditional Rayleigh quotient technique for the update of the eigenvalues, and discuss specifically the initialization of the iterative algorithm. We propose to use the homogenized equation to compute initial estimates and assess numerically the behavior of the algorithm when eigenmodes are actually localized.