A splitting iterative method for α-β generalized inverse and singular linear system

This paper deals with the case when the alpha - beta generalized inverse A(alpha,beta)((-1)) is a linear transformation, in which case we give a splitting iterative method for A(alpha,beta)((-1)) We also show that in the case of linear transformation, the alpha - beta generalized inverse A(alpha,beta)((-1)) is a {1, 2}-inverse of the matrix A with prescribed range and null space, based on which we propose a iterative method of calculating the unique alpha-approximate solution of minimal beta-norm of the system Ax = b. The results extend some previous results about the Moore-Penrose inverse A(+) and the weighted Moore-Penrose inverse A(M,N)(+). (C) 2002 Elsevier Inc. All rights reserved.