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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 | References | Similar Articles | Additional Information

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?)

  • [1] G. Schulz, ``Iterative Berechnung der reziproken Matrix,'' Z. Angew. Math. Mech. v. 13, 1933, pp. 57-59.
  • [2] R. Penrose, ``A generalized inverse for matrices,'' Proc. Cambridge Philos. Soc., v. 51, 1955, pp. 406-413. MR 16, 1082. MR 0069793 (16:1082a)
  • [3] A. Ben-Israel & A. Charnes, ``Contributions to the theory of generalized inverses,'' J. Soc. Indust. Appl. Math., v. 11, 1963, pp. 667-699. MR 0179192 (31:3441)
  • [4] W. Duck, ``Fehlerabschätzungen für das Iterationsverfahren von Schulz zur Bestimmung der Inversen einer Matrix,'' Z. Angew. Math. Mech., v. 40, 1960, pp. 192-194. MR 22 #3102. MR 0112248 (22:3102)
  • [5] A. S. Householder, Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964. MR 0175290 (30:5475)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1965-0179915-5
Article copyright: © Copyright 1965 American Mathematical Society

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