A power method for computing square roots of complex matrices

In this paper higher order convergent methods for computing square roots of nonsingular complex matrices are derived. These methods are globally convergent and are based on eigenvalue shifting and powering. Specifically, it is shown for each positive integer r ≥ 2, a convergent method of order r can be developed. These algorithms can be used to compute square roots of general nonsingular complex matrices such as computing square roots of matrices with negative eigenvalues.