Accelerated Sign-Function-Based Iterations for Matrix Square Roots with Fourth-Order Convergence

Fractal and Fractional 2026 Open access

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Authors: Shuai Wang, Zhanmeng Yang, Sommayeh Salehi, Taher Lotfi, Xiaoxi Hu, Yakun Li, Wenhao Kang, Tao Liu
DOI: 10.3390/fractalfract10020126
Cited by: 0

Abstract

Motivated by the close relationship between the matrix square root and the matrix sign function, this paper develops a new high-order iterative framework for computing the principal square root of a matrix and its inverse. The proposed approach is derived from a rational fixed-point iteration associated with a scalar nonlinear equation and is extended consistently to the matrix setting. The method is shown to be globally convergent and to achieve fourth-order convergence. Numerical experiments demonstrate that the new scheme outperforms several classical and Padé-based methods.

Fields of Study & Subjects

Matrix Theory and Algorithms Iterative Methods for Nonlinear Equations Numerical Methods and Algorithms

Publication details

Journal / source
Fractal and Fractional
Volume
10
Issue
2
Pages
126–126
Publication date
14 February 2026
Language
EN