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Source localization is based on the spectral matrix algebraic properties. Propagator, and Ermolaev-Gershman (EG) noneigenvector algorithms exhibit a low computational load. Propagator is based on the spectral matrix partitioning. EG algorithm obtains an approximation of noise subspace using an adjustable power parameter of the spectral matrix and choosing a threshold value. These algorithms are efficient in non-noisy or high signal to noise ratio (SNR) environments. However both algorithms shall be improved. Propagator is not robust to noise; EG algorithm requires the knowledge of a threshold value between largest and smallest eigenvalues, which are not available as eigendecomposition is not performed. In this paper, we aim at demonstrating the usefulness of QR and LU factorizations of the spectral matrix for these methods. Experiments show that the modified propagator and EG algorithms based on factorized spectral matrix lead to better localization results, compared to the existing methods.