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Higher-order convergent iterative method for computing the generalized inverse over Banach spaces. (English) Zbl 1291.65104

Summary: A higher-order convergent iterative method is provided for calculating the generalized inverse over Banach spaces. We also use this iterative method for computing the generalized Drazin inverse \(a^d\) in Banach algebra. Moreover, we estimate the error bounds of the iterative methods for approximating \(A^{(2)}_{T,S}\) or \(a^d\).

MSC:

65F10 Iterative numerical methods for linear systems
15A09 Theory of matrix inversion and generalized inverses
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