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We are looking for an answer to the next challenging question: is the Newton iterative rule the only iterative method for computing generalized inverses with quadratic convergence? Our answer is that it is possible to find a class of quadratically convergent iterative methods containing the Newton method. To that end, we introduce and investigate a class of iterative methods for computing the outer...
A two-step iterative method and its accelerated version for approximating outer inverse $$A^{(2)}_{T,S}$$ A T , S ( 2 ) of an arbitrary matrix A are proposed. A convergence theorem for its existence is established. The rigorous error bounds are derived. Numerical experiments involving singular square, rectangular, random matrices and a sparse matrix obtained by discretization of the...
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