  The well-known M-P (Moore-Penrose) pseudoinverse is used in several
linear-algebra applications; for example, to compute least-squares solutions of
inconsistent systems of linear equations. Irrespective of whether a given
matrix is sparse, its M-P pseudoinverse can be completely dense, potentially
leading to high computational burden and numerical difficulties, especially
when we are dealing with high-dimensional matrices. The M-P pseudoinverse is
uniquely characterized by four properties, but not all of them need to be
satisfied for some applications. In this context, Fampa and Lee (Oper. Res.
Letters, 46:605--610, 2018) and Xu, Fampa, Lee and Ponte (SIAM J. on
Optimization, to appear) propose local-search procedures to construct sparse
block-structured generalized inverses that satisfy only some of the M-P
properties. (Vector) 1-norm minimization is used to induce sparsity and to keep
the magnitude of the entries under control, and theoretical results limit the
distance between the 1-norm of the solution of the local searches and the
minimum 1-norm of generalized inverses with corresponding properties. We have
implemented several local-search procedures based on results presented in these
two papers and make here an experimental analysis of them, considering their
application to randomly generated matrices of varied dimensions, ranks, and
densities. Further, we carried out a case study on a real-world data set.
