Direct Methods for Calculating PseudoInverses

The Moore-Penrose pseudoinverse of a matrix can be defined and calculated using its singular value decomposition. There are also direct methods for computing matrix pseudo-inverses (those that avoid eigenvalue computations), but these are often rank-revealing, poorly conditioned, or otherwise limited in practice. In this paper, we demonstrate that direct methods can overcome these limitations. In particular, we reinterpret several existing direct methods and introduce new variations that are appropriate for large scale or sparse multilinear regression applications.