Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix pth root

Authors:
Oleksandr Gomilko;Dmitry B. Karp;Minghua Lin;Krystyna Zietak
Affiliations:
Faculty of Mathematics and Computer Science, Nicolas Copernicus University, 87-100 Toruń, Poland;School of Economics and Management, Far Eastern Federal University, 690950 Vladivostok, Okeanskii Prospekt 19, Russian Federation;Department of Mathematics and Statistics, University of Regina, Regina, S4S 0A2, Canada;Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzee Wyspiańskiego 27, 50-370 Wrocław, Poland
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 6
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Abstract

In this paper, we prove a conjecture on a common region of a convergence of Pade iterations for the matrix sector function. For this purpose, we show that all Pade approximants to a special case of hypergeometric function have a power series expansion with positive coefficients. Using a sharpened version of Schwarz's lemma, we also demonstrate a better estimate of the convergence speed. Our results are also applicable to a family of rational iterations for computing the matrix pth root.