© Hindawi Publishing Corp. A NOTE ON COMPUTING THE GENERALIZED INVERSE

The generalized inverse A(2)T,S 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(2)T,S has been recently developed with the condition σ(GA|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(2)T,S are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A(2)T,S, including special cases such as the weighted Moore-Penrose inverse A†M,N and the Drazin inverse AD. Numerical examples are given to illustrate our results. 2000 Mathematics Subject Classification: 15A09, 65F20. 1. Introduction. Given a complex matrix A ∈ Cm×n, any matrix X ∈ Cn×m satisfy-ing XAX = X is called a {2}-inverse of A. Let T and S be subspaces of Cn and Cm, respectively. A matrix X ∈ Cn×m is called a {2}-inverse of A with the prescribed range T and null space S, denoted by A(2)T,S, if the following conditions are satisfied