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Estimating the number of sources and locating the direction-of-arrival are important problems in array signal processing. In this paper, we propose noneigenvalues decomposition fast algorithms for radiating source detection and localization by using LU and QR factorizations of the sample cross-spectral matrix. The threshold values between the signal subspace and the noise subspace eigenvalues of the cross- spectral matrix are proposed. The developed algorithms improve the performance and reduce the computational loads of eigendecomposition based methods when the number of multiple sources is much lower than the number of array sensors. Simulations results, show the high performance and accuracy of the proposed algorithms, are presented.