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

摘要

This paper deals with the case when the α−β generalized inverse Aα,β(−1) is a linear transformation, in which case we give a splitting iterative method for Aα,β(−1). We also show that in the case of linear transformation, the α−β generalized inverse Aα,β(−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 α-approximate solution of minimal β-norm of the system Ax=b. The results extend some previous results about the Moore–Penrose inverse A+ and the weighted Moore–Penrose inverse AM,N+.