Computation of the q-th roots of circulant matrices

Subject Areas : History and biography

M. Amirfakhrian ¹ , P. Mohammadi Khanghah ²

1 - Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran
2 - Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran

Received: 2013-01-01 Accepted : 2013-01-01 Published : 2013-03-01

Keywords: Circulant matrix, Matrix q-th root, Principle q-th root of circulant matrix, Nonsingular matrix, Reduced form,

Abstract :

In this paper, we investigate the reduced form of circulant matrices and we showthat the problem of computing the q-th roots of a nonsingular circulant matrix A can bereduced to that of computing the q-th roots of two half size matrices B - C and B + C.

References:

[1] P.J. Davis, Circulant matrices, second ed., Chelsea Publishing, New York, 1994.
[2] B. Gellai, Determination of molecular symmetry coordinates using circulant matrices, journal of Molecular Structure 1 (1984) 21-26.
[3] Jesuus Gutierrez-Gutierrez, Positive integer powers of complex symmetric circulant matri- ces, Applied Mathematics and Computation 202 (2008), 877-881.
[4] C.H. Guo Nicholas J. Higham, A schur-newton method for the matrix pth root and its inverse, SIAM J, Matrix Anal. Appl 28 (2006), 788-804.
[5] N. J. Higham, Functions of matrices: Theory and computation, siam ed., Society for Industrial and Applied Mathematics, Philadelphia, 2008.
[6] B. Iannazzo, On the newton method for the matrix pth root, SIAM J, Matrix Anal. Appl 28 (2006), 503-523.
[7] M.I. Smith, A schure algorithm for computing matrix pth root, SIAM J. Matrix Anal. Appl 24 (2003), 971-989.