We first investigate the structures of the square roots of a class of circulant matrices and give classifications of the square roots of these circulant matrices. Then, we develop several algorithms for computing their square roots. We show that our algorithms are faster than the standard algorithm which is based on the Schur decomposition.
Ying Mei. "Computing the Square Roots of a Class of Circulant Matrices." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/647623