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

2011/02/19 by Minghua Lin, Karp, Dmitry B., Lin, Minghua
Computer Science · Mathematics · #33C05 #65F30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1102.3957

openalex publication_date 2011/02/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The main purpose of this paper is to give a solution to a conjecture concerning a Padé family of iterations for the matrix sector function that was recently raised by B. Laszkiewicz et al in [A Padé family of iterations for the matrix sector function and the matrix pth 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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