- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 647623, 15 pages
Computing the Square Roots of a Class of Circulant Matrices
Department of Mathematics, Lishui University, Lishui 323000, China
Received 16 August 2012; Accepted 17 October 2012
Academic Editor: Zhijun Liu
Copyright © 2012 Ying Mei. 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.
- P. J. Davis, Circulant Matrices, Chelsea Publishing, New York, NY, USA, 2nd edition, 1994.
- R. M. Gray, Toeplitz and Circulant Matrices: A Review, Stanford University Press, Stanford, Calif, USA, 2000.
- A. Mayer, A. Castiaux, and J.-P. Vigneron, “Electronic Green scattering with -fold symmetry axis from block circulant matrices,” Computer Physics Communications, vol. 109, no. 1, pp. 81–89, 1998.
- R. E. Cline, R. J. Plemmons, and G. Worm, “Generalized inverses of certain Toeplitz matrices,” Linear Algebra and its Applications, vol. 8, pp. 25–33, 1974.
- G. R. Argiroffo and S. M. Bianchi, “On the set covering polyhedron of circulant matrices,” Discrete Optimization, vol. 6, no. 2, pp. 162–173, 2009.
- N. L. Tsitsas, E. G. Alivizatos, and G. H. Kalogeropoulos, “A recursive algorithm for the inversion of matrices with circulant blocks,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 877–894, 2007.
- S. Shen and J. Cen, “On the bounds for the norms of -circulant matrices with the Fibonacci and Lucas numbers,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 2891–2897, 2010.
- Z. L. Jiang and Z. B. Xu, “A new algorithm for computing the inverse and generalized inverse of the scaled factor circulant matrix,” Journal of Computational Mathematics, vol. 26, no. 1, pp. 112–122, 2008.
- S. G. Zhang, Z. L. Jiang, and S. Y. Liu, “An application of the Gröbner basis in computation for the minimal polynomials and inverses of block circulant matrices,” Linear Algebra and its Applications, vol. 347, pp. 101–114, 2002.
- N. J. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 2008.
- G. W. Cross and P. Lancaster, “Square roots of complex matrices,” Linear and Multilinear Algebra, vol. 1, pp. 289–293, 1974.
- C. R. Johnson, K. Okubo, and R. Reams, “Uniqueness of matrix square roots and an application,” Linear Algebra and its Applications, vol. 323, no. 1–3, pp. 51–60, 2001.
- M. A. Hasan, “A power method for computing square roots of complex matrices,” Journal of Mathematical Analysis and Applications, vol. 213, no. 2, pp. 393–405, 1997.
- C. B. Lu and C. Q. Gu, “The computation of the square roots of circulant matrices,” Applied Mathematics and Computation, vol. 217, no. 16, pp. 6819–6829, 2011.
- K. D. Ikramov, “Hamiltonian square roots of skew-Hamiltonian matrices revisited,” Linear Algebra and its Applications, vol. 325, no. 1–3, pp. 101–107, 2001.
- R. Reams, “Hadamard inverses, square roots and products of almost semidefinite matrices,” Linear Algebra and its Applications, vol. 288, no. 1–3, pp. 35–43, 1999.
- G. H. Golub and C. F. van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, Md, USA, 3rd edition, 1996.