@article{Liu2025, 
author = {Ying Liu and Runqi Xue and Tao Liu and Shuai Wang and Stanford Shateyi},
title = {A quartically fast iteration solver with convergence analysis for numerically determining the sign of a matrix},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {6},
pages = {14055-14070},
keywords = {matrix sign, convergence, initial matrix, numerical scheme, Newton's solver},
url = {https://www.sciopen.com/article/10.3934/math.2025632},
doi = {10.3934/math.2025632},
abstract = {The calculation of the matrix sign function (MSF) is pivotal in numerous mathematical contexts, offering a matrix-based transformation that identifies the sign for every eigenvalue within an invertible matrix. This paper introduces a new iteration procedure tailored to effectively compute the MSF, with a particular focus on expanding the order of convergence. Our proposed solver achieves fourth-order convergence, rendering it effective for a broad spectrum of matrices. Numerical experiments for both real and complex matrices are included to support the derivations.}
}