Convergence theory of efficient parametric iterative methods for solving the Yang-Baxter-like matrix equation
ISSN: 0264-4401
Article publication date: 29 November 2024
Issue publication date: 7 January 2025
Abstract
Purpose
In this study, we present a novel parametric iterative method for computing the polar decomposition and determining the matrix sign function.
Design/methodology/approach
This method demonstrates exceptional efficiency, requiring only two matrix-by-matrix multiplications and one matrix inversion per iteration. Additionally, we establish that the convergence order of the proposed method is three and four, and confirm that it is asymptotically stable.
Findings
In conclusion, we extend the iterative method to solve the Yang-Baxter-like matrix equation. The efficiency indices of the proposed methods are shown to be superior compared to previous approaches.
Originality/value
The efficiency and accuracy of our proposed methods are demonstrated through various high-dimensional numerical examples, highlighting their superiority over established methods.
Keywords
Acknowledgements
The authors wish to express their gratitude to the editor and anonymous reviewers for helpful remarks and suggestions.
Citation
Erfanifar, R., Sayevand, K. and Hajarian, M. (2025), "Convergence theory of efficient parametric iterative methods for solving the Yang-Baxter-like matrix equation", Engineering Computations, Vol. 42 No. 1, pp. 255-276. https://doi.org/10.1108/EC-12-2023-0965
Publisher
:Emerald Publishing Limited
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