An Accelerated Sixth-Order Procedure to Determine the Matrix Sign Function Computationally

Shuai Wang, Ziyang Wang, Wu Xie, Yunfei Qi and Tao Liu ()
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Shuai Wang: Foundation Department, Changchun Guanghua University, Changchun 130033, China
Ziyang Wang: Sydney Smart Technology College, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Wu Xie: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, China
Yunfei Qi: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, China
Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Mathematics, 2025, vol. 13, issue 7, 1-12

Abstract: The matrix sign function has a key role in several applications in numerical linear algebra. This paper presents a novel iterative approach with a sixth order of convergence to efficiently compute this function. The scheme is constructed via the employment of a nonlinear equations solver for simple roots. Then, the convergence of the extended matrix procedure is investigated to demonstrate the sixth rate of convergence. Basins of attractions for the proposed solver are given to show its global convergence behavior as well. Finally, the numerical experiments demonstrate the effectiveness of our approach compared to classical methods.

Keywords: invertible matrix; sign; starting value; iterative methods; sixth order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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