A Parallel algorithm for principal nth roots of matrices

An iterative algorithm for computing the principal nth root of a positive deenite matrix is presented. The algorithm is based on the Gauss-Legendre approximation of a deenite integral. We p resent a parallelization in which we use as many processors as the order of the approximation. An analysis of the error introduced at each step of the iteration indicates that the algorithm converges more rapidly as the order of the approximation thus, the number of processors increases. We describe the results of our implementation on an 8-processor Meiko CS-2, comparing the parallel algorithm to the fastest sequential algorithm, which is the Hoskins-Walton method.