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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Penrose, R.: A generalized inverse for matrices. Proc. of Cambridge Philos. Soc.51, 406–413 (1955).
Tewarson, R. P.: A direct method for generalized matrix inversion. SIAM J. Numer. Anal.2, 499–507 (1967).
Osborne, E. E.: Smallest least squares solution to linear equations. SIAM J. Numer. Anal.2, 300–307 (1965).
Jordan, T. L.: Experiments of error growth associated with some linear leastsquares procedures. Math. Comp.22, 579–588 (1968).
Rice, J. H.: Experiments on Gram-Schmidt orthogonalization. Math. Comp.20, 325–328 (1966).
Björck, A.: Solving linear least squares problems by Gram-Schmidt orthogonalization. BIT1, 1–21 (1967).
Rust, G., W. R. Burrus, andC. Schneeberger: A simple algorithm for computing the generalized inverse of a matrix. Comm. ACM9, 381–387 (1966).
Penrose, R.: On best approximate solutions of linear matrix equations. Proc. Cambridge Philos. Soc.52, 17–19 (1956).
Wilkinson, J. H.: The Algebraic Eigenvalue Problem. Oxford: University Press. 1965.
Tewarson, R. P.: A computational method for evaluation generalized inverses. Computer J.10, 411–413 (1968).
Tewarson, R. P.: On computing generalized inverses. Computing4, 139–152 (1969).
Author information
Authors and Affiliations
Additional information
This work was supported in part by the National Aeronautics and Space Administration, Washington, D.C., under Grant NCR-33-015-013.
Rights and permissions
About this article
Cite this article
Tewarson, R.P. On two direct methods for computing generalized inverses. Computing 7, 236–239 (1971). https://doi.org/10.1007/BF02242350
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02242350