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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 262034, 12 pages
doi:10.1155/2012/262034
Research Article
Successive Matrix Squaring Algorithm for Computing the Generalized Inverse
1College of Science, Guangxi University for Nationalities, Nanning 530006, China
2Guangxi Key Laborarory of Hybrid Computational and IC Design Analysis, Nanning 530006, China
Received 12 June 2012; Accepted 29 November 2012
Academic Editor: J. Biazar
Copyright © 2012 Xiaoji Liu and Yonghui Qin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- A. Ben-Israel and T. N. E. Greville, Generalized Inverses, Theory and Applications, vol. 15 of CMS Books in Mathematics, Springer, New York, NY, USA, 2nd edition, 2003. View at Zentralblatt MATH
- A. J. Getson and F. C. Hsuan, {2}-Inverses and Their Statistical Application, vol. 47 of Lecture Notes in Statistics, Springer, New York, NY, USA, 1988. View at Publisher · View at Google Scholar
- B. Codenotti, M. Leoncini, and G. Resta, “Repeated matrix squaring for the parallel solution of linear systems,” in PARLE '92 Parallel Architectures and Languages Europe, vol. 605 of Lecture Notes in Computer Science, pp. 725–732, Springer, Berlin, Germany, 1992. View at Publisher · View at Google Scholar
- Y. Wei, “Successive matrix squaring algorithm for computing the Drazin inverse,” Applied Mathematics and Computation, vol. 108, no. 2-3, pp. 67–75, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Y. Wei, H. Wu, and J. Wei, “Successive matrix squaring algorithm for parallel computing the weighted generalized inverse ,” Applied Mathematics and Computation, vol. 116, no. 3, pp. 289–296, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- P. S. Stanimirović and D. S. Cvetković-Ilić, “Successive matrix squaring algorithm for computing outer inverses,” Applied Mathematics and Computation, vol. 203, no. 1, pp. 19–29, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Miladinović, S. Miljković, and P. Stanimirović, “Modified SMS method for computing outer inverses of Toeplitz matrices,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3131–3143, 2011. View at Publisher · View at Google Scholar
- D. S. Djordjević and P. S. Stanimirović, “On the generalized Drazin inverse and generalized resolvent,” Czechoslovak Mathematical Journal, vol. 51(126), no. 3, pp. 617–634, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- D. S. Djordjević and P. S. Stanimirović, “Splittings of operators and generalized inverses,” Publicationes Mathematicae Debrecen, vol. 59, no. 1-2, pp. 147–159, 2001. View at Zentralblatt MATH
- X. Liu, Y. Yu, and C. Hu, “The iterative methods for computing the generalized inverse of the bounded linear operator between Banach spaces,” Applied Mathematics and Computation, vol. 214, no. 2, pp. 391–410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- X.-Z. Chen and R. E. Hartwig, “The hyperpower iteration revisited,” Linear Algebra and Its Applications, vol. 233, pp. 207–229, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- B. Zheng and G. Wang, “Representation and approximation for generalized inverse : revisited,” Journal of Applied Mathematics & Computing, vol. 22, no. 3, pp. 225–240, 2006. View at Publisher · View at Google Scholar