The generalized inverse of a matrix is a -inverse of with the prescribed range and null space . A representation for the generalized inverse
has been recently developed with the condition
, where is a matrix with and. In this note, we remove the above condition. Three types of iterative methods for are presented if is a subset of the open right half-plane and they are extensions of existing computational procedures of , including special cases such as the weighted Moore-Penrose inverse and the Drazin inverse . Numerical examples are given to illustrate our results.