Computing the square roots of matrices with central symmetry (Q876654)

The reduced forms of centrosymmetric, skew-centrosymmetric and centro-Hermitian matrices are exploited to study the structure of square roots of such matrices and to design algorithms for computing those square roots. A new structured algorithm to compute the square root is proposed that is approximately 5.5 times cheaper than the standard one. In the case of centro-Hermitian matrices, the corresponding structured algorithm is approximately eight times cheaper than the standard one. The stability and the accuracy of the algorithms proposed are discussed.