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

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Publicado en:Engineering Computations vol. 42, no. 1 (2025), p. 255-276
Autor principal: Erfanifar, Raziyeh
Otros Autores: Sayevand, Khosro, Hajarian, Masoud
Publicado:
Emerald Group Publishing Limited
Materias:
Asymptotic methods
Statistical mechanics
Convergence
Quantum theory
Theoretical physics
Iterative methods
Equilibrium
Efficiency
Decomposition
Statistical physics
Mathematics
Eigenvalues
Quantum field theory
Methods
Mathematicians
Acceso en línea:Citation/Abstract
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Resumen:PurposeIn this study, we present a novel parametric iterative method for computing the polar decomposition and determining the matrix sign function.Design/methodology/approachThis 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.FindingsIn 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/valueThe efficiency and accuracy of our proposed methods are demonstrated through various high-dimensional numerical examples, highlighting their superiority over established methods.
ISSN:0264-4401
1758-7077
DOI:10.1108/EC-12-2023-0965
Fuente:ABI/INFORM Global