Higher-order convergent iterative method for computing the generalized inverse and its application to Toeplitz matrices

The main aim of this paper is to provide a higher-order convergent iterative method in order to calculate the generalized inverse of a given matrix. We extend the iterative method proposed in Li et al. [W.G. Li, Z. Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Applied Mathematics and Computation 215 (2010) 3433-3442] to compute the {2}-inverse, generalized inverse -inverse and {2,4}-inverse. Moreover, we modify the iterative method to compute the generalized inverse of Toeplitz matrices by using the displacement theory.