Convergence analysis of a Pad\'{e} family of iterations for the matrix sector function
Classical Analysis and ODEs
2011-02-22 v1 Numerical Analysis
Abstract
The main purpose of this paper is to give a solution to a conjecture concerning a Pad\'{e} family of iterations for the matrix sector function that was recently raised by B. Laszkiewicz et al in [A Pad\'{e} family of iterations for the matrix sector function and the matrix th root, Numer. Linear Algebra Appl. 2009; 16:951-970]. Using a sharpened version Schwarz's lemma, we also demonstrate a strengthening of the conjecture.
Keywords
Cite
@article{arxiv.1102.3957,
title = {Convergence analysis of a Pad\'{e} family of iterations for the matrix sector function},
author = {Dmitry B. Karp and Minghua Lin},
journal= {arXiv preprint arXiv:1102.3957},
year = {2011}
}
Comments
8 pages, no figures