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General Forms for the Recursive Determination of Generalized Inverses: Unified Approach

Author

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  • F. E. Udwadia

    (University of Southern California)

  • R. E. Kalaba

    (University of Southern California)

Abstract

Results for the recursive determination of different types of generalized inverses of a matrix are presented for the case of the addition of a block-column matrix of arbitrary size. Using a unifying underlying theme, results for the generalized inverse, least-square generalized inverse, minimum norm generalized inverse, and Moore–Penrose inverse are included.

Suggested Citation

  • F. E. Udwadia & R. E. Kalaba, 1999. "General Forms for the Recursive Determination of Generalized Inverses: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 509-521, June.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:3:d:10.1023_a:1021781918962
    DOI: 10.1023/A:1021781918962
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    References listed on IDEAS

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    1. F. E. Udwadia & R. E. Kalaba, 1997. "An Alternative Proof of the Greville Formula," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 23-28, July.
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    Cited by:

    1. K. Ramanathan & K. C. Sivakumar, 2009. "Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 189-196, January.
    2. T. Kurmayya & K. C. Sivakumar, 2008. "Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 201-207, October.
    3. K. C. Sivakumar & J. M. Swarna, 2009. "Linear Optimization with Box Constraints in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 377-387, May.

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    1. K. C. Sivakumar & J. M. Swarna, 2009. "Linear Optimization with Box Constraints in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 377-387, May.
    2. T. Kurmayya & K. C. Sivakumar, 2008. "Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 201-207, October.
    3. K. Ramanathan & K. C. Sivakumar, 2009. "Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 189-196, January.

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