A Higher Order Iterative Method for Computing the Drazin Inverse

Abstract

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper.

High-Order Iterative Methods for the DMP Inverse

“…The iterative method given in (4) is applied to compute the Drazin inverse by [21]. Here, we use the sequence of iterative…”

“…So far, there are few results on computation of the DMP inverse by the iterative methods given in [17][18][19][20][21][22]. Recently, a family of higher-order convergent iterative methods are developed in [23] and applied to compute the Moore-Penrose inverse; the method is extended to compute the generalized inverse in [20].…”

Iterative Method to Find Core-EP Inverse

“…In the recent years, many have attempted to improvise these iterative methods to find MoorePenrose inverse, Drazin inverse and outer inverses with specific column space and row space. A few examples in this regard are work by Stanimirović with his collaborators (see [12,13,16,17]) and others (see, [5,6,11,18,19]). In this article, inspired by Stanimirović's work, we consider core-EP inverse as a special case of an outer inverse to propose an iterative method and discuss its convergence.…”

A Class of Kung–Traub-Type Iterative Algorithms for Matrix Inversion

“…They managed to extend Newton's method to compute matrix inverses of regular matrices. Some further discussions, extensions and modifications have then been done for computing inner inverses in [6], Drazin inverse in [7], Moore-Penrose inverse in [8], weighted Moore-Penrose inverse in [9] and interval versions in [10].…”