Algorithms for computing nth roots and the matrix sector function of nonsingular complex matrices

New fast convergent methods for computing the principal nth roots, and matrix sector functions of nonsingular complex matrices are developed. The main features of these methods in addition to higher order convergence are (1) they are power-like methods and thus they are stable and self-correcting, (2) they are globally convergent in that they converge from a broad sets of initial conditions, and (3) they are less sensitive to sector boundary. Additionally the techniques of this paper allow for computing a set of projectors onto some of the subeigenspaces which can be used to compute the number of eigenvalues in a given sector and to compute more nth roots of a given matrix. Several examples are also included to illustrate the performance of the proposed algorithms.