Parallel solution of large sparse linear least squares problems

In the recent paper [Duff I. et al, SIAM J. Sci. Comp., 37(3) (2015), A1248-A1269] the authors proposed an interesting procedure for the parallel solution of large, sparse consistent linear systems of equations. In this respect, according to a reordering of the initial matrix, the authors extend it by obtaining mutually orthogonal row blocks, which give them the possibility to get a solution through only one Block Cimmino iteration. We present in our paper an extension of this procedur to inconsistent large sparse linear least squares problems. Through this extension applications of the method are well suited for problems arising in Compressed Sensing, Image Reconstruction in Computerized Tomography and Rigid Body Dynamics.