Spectrum sensing of primary users under very low signal-to-noise ratio (SNR) and noise uncertainty is crucial for cognitive radio (CR) systems. To overcome the drawbacks of weak signal and noise uncertainty, eigenvalue-based spectrum sensing methods have been proposed for advanced CRs. However, one pressing disadvantage of eigenvalue-based spectrum sensing algorithms is their high computational complexity, which is due to the calculation of the covariance matrix and its eigenvalues. In this study, power, inverse power and fast Cholesky methods for eigenvalue computation are investigated as potential methods for reducing the computational complexity.