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- W2284392585 abstract "In this paper we consider the Padé family of iterations [B. Laszkiewicz, K. Ziȩtak, A Padé family of iterations for the matrix sector function and the matrix p th root, Numer. Linear Algebra Appl. 16 (2009) 951–970] and a new dual Padé family of iterations for computing the principal p th root of a matrix, including the Newton and Halley methods as particular cases. We prove convergence of iterations of these families in certain regions. We also propose a new dual Padé family of iterations for computing the matrix p -sector function and we determine a certain region of convergence. For this purpose we study properties of the Padé approximants to the function ( 1 − z ) − 1 / p . We show a connection of the series expansion with respect to B of the iterates, generated by iterations of the dual Padé family for computing the matrix p th root ( I − B ) 1 / p , with binomial scalar expansion of ( 1 − b ) 1 / p ." @default.
- W2284392585 created "2016-06-24" @default.
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- W2284392585 date "2014-12-01" @default.
- W2284392585 modified "2023-10-17" @default.
- W2284392585 title "The dual Padé families of iterations for the matrix pth root and the matrix p-sector function" @default.
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- W2284392585 doi "https://doi.org/10.1016/j.cam.2013.07.021" @default.
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