To read this content please select one of the options below:

Convergence theory of efficient parametric iterative methods for solving the Yang-Baxter-like matrix equation

Raziyeh Erfanifar (Department of Mathematics, Shahid Beheshti University, Tehran, Iran)
Khosro Sayevand (Malayer University, Malayer, Iran)
Masoud Hajarian (Department of Mathematics, Shahid Beheshti University, Tehran, Iran)

Engineering Computations

ISSN: 0264-4401

Article publication date: 29 November 2024

Issue publication date: 7 January 2025

60

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

Copyright © 2024, Emerald Publishing Limited

Related articles