Elimination with Noninvertible Pivots

A method for carrying out the Gauss elimination solution of linear systems is presented. The novelty arises from the fact that the pivot matrices are not required to be invertible, so that, for example, a scalar pivot may be zero, and a matrix pivot may be rectangular or singular. The need to execute the elimination algorithm in such circumstances arose in connection with a finite element solution of the Navier-Stokes equations in velocity-pressure variables. This application is briefly discussed, as is a method for the implementation of the algorithm.