The hyperpower iteration revisited

DOI10.1016/0024-3795(94)00076-XzbMath0848.65021MaRDI QIDQ1906783

Robert E. Hartwig, Xu-Zhou Chen

Publication date: 25 February 1996

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

convergencehyperpower methodidempotent matricesmatrix inversegeneralised inverses

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Iterative numerical methods for linear systems (65F10)

Related Items (11)

The stability of formulae of the Gohberg-Semencul-Trench type for Moore-Penrose and group inverses of Toeplitz matrices ⋮ The Picard iteration and its application ⋮ The iterative methods for computing the generalized inverse \(A^{(2)}_{T,S}\) of the bounded linear operator between Banach spaces ⋮ The computation of Drazin inverse and its application in Markov chains ⋮ Successive matrix squaring algorithm for computing the generalized inverse \(A^{(2)}_{T, S}\) ⋮ Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\) ⋮ On hyperpower family of iterations for computing outer inverses possessing high efficiencies ⋮ Further results on iterative methods for computing generalized inverses ⋮ A geometrical approach on generalized inverses by Neumann-type series ⋮ Successive matrix squaring algorithm for computing the Drazin inverse ⋮ Representation and approximation for the Drazin inverse \(A^{(\text{d})}\)

Cites Work

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• Numerical algorithms for the Moore-Penrose inverse of a matrix: iterative methods
• Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method
• On generalized inverses and on the uniform convergence of \((I-\beta K)_ n\) with application to iterative methods
• Anwendung des Schulz‐Verfahrens zur Nachkorrektur einer näherungsweise berechneten verallgemeinerten Inversen einer Matrix
• An Iterative Method for Computing the Generalized Inverse of an Arbitrary Matrix
• A Note on an Iterative Method for Generalized Inversion of Matrices
• On Iterative Computation of Generalized Inverses and Associated Projections
• On the Numerical Properties of an Iterative Method for Computing the Moore–Penrose Generalized Inverse

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