Convergence analysis of a Padé family of iterations for the matrix sector function

Details Convergence analysis of a Padé family of iterations for the matrix sector function Convergence analysis of a Padé family of iterations for the matrix sector function

2011-02-19

arxiv.org/abs/1102.3957v1

Mathematics

Classical Analysis and ODEs

8 pages, no figures

Scientific paper

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 $p$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.

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