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

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Publicado en:Mathematics vol. 13, no. 21 (2025), p. 3370-3388
Autor principal: Zhu Jiameihui
Otros Autores: Li, Yutong, Li, Yilin, Liu, Tao, Ma, Qiang
Publicado:
MDPI AG
Materias:
Computational mathematics
Approximation
Iterative algorithms
Data science
Roots
Eigenvalues
Convergence
Algorithms
Iterative methods
Efficiency
Linear algebra
Acceso en línea:Citation/Abstract
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Resumen: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.
ISSN:2227-7390
DOI:10.3390/math13213370
Fuente:Engineering Database