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Mathematics of Computation

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An iterative method for computing the generalized inverse of an arbitrary matrix


Author: Adi Ben-Israel
Journal: Math. Comp. 19 (1965), 452-455
MSC: Primary 65.35
DOI: https://doi.org/10.1090/S0025-5718-1965-0179915-5
MathSciNet review: 0179915
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Abstract: The iterative process, ${X_{n + 1}} = {X_n}(2I - A{X_n})$, for computing ${A^{ - 1}}$, is generalized to obtain the generalized inverse.


References [Enhancements On Off] (What's this?)

    G. Schulz, “Iterative Berechnung der reziproken Matrix,” Z. Angew. Math. Mech. v. 13, 1933, pp. 57–59.
  • R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. MR 69793
  • A. Ben-Israel and A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math. 11 (1963), 667–699. MR 179192
  • W. Dück, Fehlerabschätzungen für das Iterationsverfahren von Schulz zur Bestimmung der Inversen einer Matrix, Z. Angew. Math. Mech. 40 (1960), 192–194 (German). MR 112248, DOI https://doi.org/10.1002/zamm.19600400410
  • Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0175290

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Article copyright: © Copyright 1965 American Mathematical Society