Convergence analysis of a Padé family of iterations for the matrix sector function
arXiv:1102.3957h-index: 19
Originality Synthesis-oriented
AI Analysis
Provides theoretical convergence guarantees for a numerical method used in matrix computations, but the result is incremental.
The paper resolves a conjecture about the convergence of a Padé family of iterations for the matrix sector function and strengthens it using a sharpened Schwarz lemma.
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 $p$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.