A Note on Computing the Generalized Inverse A^(2)_{T,S} of a Matrix A

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 (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) 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 T,S (2), 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

A characterization and representation of the generalized inverse A(2)T,S and its applications

AbstractThis paper presents an explicit expression for the generalized inverse A(2)T,S. Based on this, we established the characterization, the representation theorem and the limiting process for A(2)T,S. As an application, we estimate the error bound of the iterative method for approximating A(2)T,S