A Note on the Square Roots of a Class of Circulant Matrices

作者:Zhang, Ying*; Zhang, Huisheng; Chen, Guoyan
来源:Journal of Applied Mathematics, 2013, 2013: 601243.
DOI:10.1155/2013/601243

摘要

We prove that any k-circulant matrix and any even order skew k-circulant matrix are diagonalizable for any k is an element of C. Then, we propose two algorithms for computing the square roots of the k-circulant matrix and the skew k-circulant matrix, respectively. In particular, we show that the square roots of the k-circulant matrix are still k-circulant matrices. Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method.

全文