In this paper, we present a new array processing scheme which allows fast and parallel computation of the signal (principal) and noise (minor) subspaces. The proposed method, named Generalized Minimum Noise Subspace (GMNS), is a generalization of the minimum noise subspace concept, introduced first for blind channel identification, subject to an availability of a fixed number of parallel computational units. In addition, we introduce different batch and adaptive algorithms for fast and parallel computation of the noise as well as the signal subspaces. The GMNS cost and its related estimation accuracy are investigated by theoretical and numerical analyses. The latter shows that the GMNS represents an excellent trade-off between the computational gain and estimation loss as compared to the standard subspace methods.