Abstract
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 AT,S(2),{2,3}-inverse and {2,4}-inverse. Moreover, we modify the iterative method to compute the generalized inverse AT,S(2) of Toeplitz matrices by using the displacement theory.
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