Parallel solution of large sparse linear least squares problems
Provides a parallel solution for large sparse least squares problems, extending prior work to inconsistent systems, which is incremental in nature.
Extended a parallel solver for consistent sparse linear systems to handle inconsistent large sparse linear least squares problems, enabling efficient solution in one Block Cimmino iteration. The method is applicable to compressed sensing, image reconstruction, and rigid body dynamics.
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.