Parallel solution of large sparse linear least squares problems

TL;DR

This paper extends a parallel method for solving large sparse linear least squares problems, originally designed for consistent systems, making it applicable to inconsistent systems in fields like compressed sensing and image reconstruction.

Contribution

It introduces an extension of a parallel solution method to handle inconsistent large sparse least squares problems, broadening its applicability.

Findings

Effective for large sparse problems in compressed sensing

Applicable to image reconstruction and rigid body dynamics

Enables solution with a single Block Cimmino iteration

Abstract

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.