Work

Fourth-Order Iterative Algorithms for the Simultaneous Calculation of Matrix Square Roots and Their Inverses

Year: 2025

Type: article

Abstract: This paper develops and analyzes new high-order iterative schemes for the effective evaluation of the matrix square root (MSR). By leveraging connections between the matrix sign function and the MSR, we design stable algorithms that exhibit fourth-order convergence under mild spectral conditions. Detailed error bounds and convergence analyses are provided, ensuring both theoretical rigor and numerical reliability. A comprehensive set of numerical experiments, conducted across structured and large-scale test matrices, demonstrates the superior performance of the proposed methods compared to classical approaches, both in terms of computational efficiency and accuracy. The results confirm that the proposed iterative strategies provide robust and scalable tools for practical applications requiring repeated computation of matrix square roots.

Source: Mathematics

DOI: 10.3390/math13213370

Authors: Jiameihui Zhu, Yutong Li, Yilin Li, Tao Liu, Qiang Ma

Institutions: Northeastern University, Harbin Institute of Technology

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Division of Graduate Education