Abstract:When A is a matrix with all eigenvalues in the disk |z −1| < 1, the principal pth root of A can be computed by Schröder's method, among many other methods. In this paper we present a further study of Schröder's method for the matrix pth root, through an examination of power series expansions of some sequences of scalar functions. Specifically, we obtain a new and informative error estimate for the matrix sequence generated by the Schröder's method, a monotonic convergence result when A is a nonsingular M -matr… Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.