An algorithm for the calculation of the pseudo-inverse of a singular matrix is derived. The method is motivated by Wiener-Kalman filtering theory and uses successive "observations" to update the "estimation" of the pseudo-inverse. Illustrative and numerical examples are given so that the speed and accuracy of the method may be compared with ordinary inversion. Although the speed of the method may be made to approach that of ordinary inversion, to achieve reasonable accuracy double precision arithmetic must be employed with a consequent reduction in speed.