Energy based spectrum sensing detectors is optimal in terms of computational complexity but they have certain limitations of their dependence upon noise. In contrast eigenvalue based algorithms do not depend upon noise uncertainty. Eigenvalue based algorithms are computationally complex as compared to energy detection method. Its complexity comes from two steps, the decomposition of the covariance matrix and the computation of eigenvalues. The computation of eigenvalues still is an open field for research. In this paper, we propose fast iterative algorithms to handle eigenvalue problems for eigenvalue based spectrum sensing detections. The proposed algorithm reduces the complexity of the eigenvalue based spectrum sensing techniques to O(L). Simulations based on the wireless microphone signals are presented to verify the proposed.