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The computation of the square roots of circulant matrices. (English) Zbl 1229.65068
The authors construct the reduced forms of circulant matrices and quasi-skew circulant matrices. Then they show that the problem of computing the circulant square roots of a circulant matrix $A$ can be reduced to that of computing the square roots of two half size matrices $B-C$ and $B+C$. Two efficient algorithms are presented to compute their square roots. Those methods are faster than the traditional algorithm which is based on the Schur decomposition. They further consider circulant $H$-matrices with positive diagonal entries and develop two algorithms for computing their principal square roots. Those two algorithms are based on $LL$ iteration and the modified Schulz iterative method, respectively. Some numerical experiments are presented.

##### MSC:
 65F30 Other matrix algorithms 15A24 Matrix equations and identities
##### Software:
mctoolbox; testmatrix
Full Text:
##### References:
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