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On two direct methods for computing generalized inverses

Über zwei direkte Methoden zur Berechnung der generalisierten Inversen

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Summary

Two methods for computing theMoore-Penrose generalized inverse and explicit expressions for the (1, 2, 3) and the (1, 2, 4) generalized inverses of a matrix are given.

Zusammenfassung

Es werden zwei Methoden zur Berechnung der generalisiertenMoore-Penrose-Inversen und explizite Ausdrücke für die generalisierten Inversen (1, 2, 3) und (1, 2, 4) einer Matrix gebracht.

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References

  1. Penrose, R.: A generalized inverse for matrices. Proc. of Cambridge Philos. Soc.51, 406–413 (1955).

    Google Scholar 

  2. Tewarson, R. P.: A direct method for generalized matrix inversion. SIAM J. Numer. Anal.2, 499–507 (1967).

    Google Scholar 

  3. Osborne, E. E.: Smallest least squares solution to linear equations. SIAM J. Numer. Anal.2, 300–307 (1965).

    Google Scholar 

  4. Jordan, T. L.: Experiments of error growth associated with some linear leastsquares procedures. Math. Comp.22, 579–588 (1968).

    Google Scholar 

  5. Rice, J. H.: Experiments on Gram-Schmidt orthogonalization. Math. Comp.20, 325–328 (1966).

    Google Scholar 

  6. Björck, A.: Solving linear least squares problems by Gram-Schmidt orthogonalization. BIT1, 1–21 (1967).

    Google Scholar 

  7. Rust, G., W. R. Burrus, andC. Schneeberger: A simple algorithm for computing the generalized inverse of a matrix. Comm. ACM9, 381–387 (1966).

    Google Scholar 

  8. Penrose, R.: On best approximate solutions of linear matrix equations. Proc. Cambridge Philos. Soc.52, 17–19 (1956).

    Google Scholar 

  9. Wilkinson, J. H.: The Algebraic Eigenvalue Problem. Oxford: University Press. 1965.

    Google Scholar 

  10. Tewarson, R. P.: A computational method for evaluation generalized inverses. Computer J.10, 411–413 (1968).

    Google Scholar 

  11. Tewarson, R. P.: On computing generalized inverses. Computing4, 139–152 (1969).

    Google Scholar 

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Additional information

This work was supported in part by the National Aeronautics and Space Administration, Washington, D.C., under Grant NCR-33-015-013.

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Tewarson, R.P. On two direct methods for computing generalized inverses. Computing 7, 236–239 (1971). https://doi.org/10.1007/BF02242350

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  • DOI: https://doi.org/10.1007/BF02242350

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