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

• Autores: Oleksandr Gomilko, Dmitry B. Karp, Minghua Lin, Krystyna Zietak
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 236, Nº 17, 2012, págs. 4410-4420
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.04.007
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• Resumen

  • In this paper, we prove a conjecture on a common region of a convergence of Padé iterations for the matrix sector function. For this purpose, we show that all Padé 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.