Computing the Moore-Penrose Inverse of a Matrix Through Symmetric Rank-One Updates
Xuzhou Chen, Jun Ji
DOI: 10.4236/ajcm.2011.13016   PDF   HTML     7,217 Downloads   15,625 Views   Citations


This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexity of the method is analyzed and a numerical example is included. A variant of the algorithm with lower computational complexity is also proposed. Both algorithms are tested on randomly generated matrices. Numerical performance confirms our theoretic results.

Share and Cite:

X. Chen and J. Ji, "Computing the Moore-Penrose Inverse of a Matrix Through Symmetric Rank-One Updates," American Journal of Computational Mathematics, Vol. 1 No. 3, 2011, pp. 147-151. doi: 10.4236/ajcm.2011.13016.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] X. Chen, “The Generalized Inverses of Perturbed Matrices,” International Journal of Computer Mathematics, Vol. 41, No. 3-4, 1992, pp. 223-236.
[2] T. N. E. Greville, “Some Applications of Pseudoinverse of a Matrix,” SIAM Review, Vol. 2, No. 1, 1960, pp. 15-22. doi:10.1137/1002004
[3] S. R. Vat-sya and C. C. Tai, “Inverse of a Perturbed Matrix,” International Journal of Computer Mathematics, Vol. 23, No. 2, 1988, pp. 177-184. doi:10.1080/00207168808803616
[4] Y. Wei, “Expression for the Drazin Inverse of a 2 × 2 Block Matrix,” Linear and Multilinear Algebra, Vol. 45, 1998, pp. 131-146. doi:10.1080/03081089808818583
[5] S. L. Campbell and C. D. Meyer, “Generalized Inverses of Linear Transformations,” Pitman, London, 1979.
[6] G. R. Wang, Y. Wei and S. Qiao, “Generalized Inverses: Theory and Computations,” Science Press, Beijing/New York, 2004.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.