arXiv Analytics

Sign in

arXiv:1807.04251 [math.NA]AbstractReferencesReviewsResources

A study of Schröder's method for the matrix $p$th root using power series expansions

Chun-Hua Guo, Di Lu

Published 2018-07-11Version 1

When $A$ is a matrix with all eigenvalues in the disk $|z-1|<1$, the principal $p$th root of $A$ can be computed by Schr\"oder's method, among many other methods. In this paper we present a further study of Schr\"oder's method for the matrix $p$th 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 Schr\"oder's method, a monotonic convergence result when $A$ is a nonsingular $M$-matrix, and a structure preserving result when $A$ is a nonsingular $M$-matrix or a real nonsingular $H$-matrix with positive diagonal entries.

Related articles:
arXiv:1903.06268 [math.NA] (Published 2019-03-14)
Rational Minimax Iterations for Computing the Matrix $p$th Root
arXiv:1611.02848 [math.NA] (Published 2016-11-09)
A cost-efficient variant of the incremental Newton iteration for the matrix $p$th root
arXiv:1506.03848 [math.NA] (Published 2015-06-11)
On evaluation of the Heun functions