{
"id": "1807.04251",
"version": "v1",
"published": "2018-07-11T17:14:46.000Z",
"updated": "2018-07-11T17:14:46.000Z",
"title": "A study of SchrÃ¶der's method for the matrix $p$th root using power series expansions",
"authors": [
"Chun-Hua Guo",
"Di Lu"
],
"categories": [
"math.NA"
],
"abstract": "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.",
"revisions": [
{
"version": "v1",
"updated": "2018-07-11T17:14:46.000Z"
}
],
"analyses": {
"keywords": [
"power series expansions",
"th root",
"schrÃ¶ders method",
"monotonic convergence result",
"real nonsingular"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}