The generalized inverse A   T , S   ( 2 ) of a matrix A is a { 2 } -inverse of A with the prescribed range T and null space S . A representation for the generalized inverse A   T , S   ( 2 ) has been recently developed with the condition σ   ( G A |   T ) ⊂ ( 0 , ∞ ) , where G is a matrix with R ( G ) = T and N ( G ) = S . In this note, we remove the above condition. Three types of iterative methods for A   T , S   ( 2 ) are presented if σ ( G A | T ) is a subset of the open right half-plane and they are extensions of existing computational procedures of A   T , S   ( 2 ) , including special cases such as the weighted Moore-Penrose inverse A   M , N   † and the Drazin inverse A D . Numerical examples are given to illustrate our results.