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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An iterative method for computing the generalized inverse of an arbitrary matrix
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by Adi Ben-Israel PDF
Math. Comp. 19 (1965), 452-455 Request permission

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
    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 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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Additional Information
  • © Copyright 1965 American Mathematical Society
  • 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