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Computation of the q-th roots of circulant matrices | ||
Journal of Linear and Topological Algebra | ||
مقاله 6، دوره 02، شماره 01، خرداد 2013، صفحه 59-65 اصل مقاله (118.24 K) | ||
نوع مقاله: Research Paper | ||
نویسندگان | ||
M. Amirfakhrian؛ P. Mohammadi Khanghah* | ||
Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran | ||
چکیده | ||
In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C. | ||
کلیدواژهها | ||
Circulant matrix؛ Matrix q-th root؛ Principle q-th root of circulant matrix؛ Nonsingular matrix؛ Reduced form | ||
مراجع | ||
[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. | ||
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