Generalized conditioned inverse
N.E. Ligterink · University of Twente Research Information · 2007
The generalized conditioned inverse is an order $N^3$ method to generate an inverse of a singular or near singular matrix, using complete pivoting. Instead of eigenvectors, the inverse is expressed in terms of a left and right representative space, such that the dimension of the problem is reduced in a trivial manner, limiting the bookkeeping. The null space vectors can be constructed to test the existence of a solution.