Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications DOI Creative Commons
Abdur Rehman,

Muhammad Zia Ur Rahman,

Asim Ghaffar

и другие.

AIMS Mathematics, Год журнала: 2024, Номер 9(10), С. 26371 - 26402

Опубликована: Янв. 1, 2024

<p>In applied and computational mathematics, quaternions are fundamental in representing three-dimensional rotations. However, specific types of quaternionic linear matrix equations remain few explored. This study introduces new their necessary sufficient conditions for solvability. We employ a methodology involving lemmas ranks coefficient matrices to develop novel algorithm. algorithm is validated through numerical examples, showing its applications advanced fields. In control theory, these used analyzing systems, particularly spacecraft attitude aerospace engineering arms robotics. quantum computing, model gates transformations, which important algorithms error correction, contributing the development fault-tolerant computers. signal processing, enhance multidimensional filtering noise reduction, with color image processing radar analysis. extend our include cases $ \eta $-Hermitian i-Hermitian solutions. Our work represents an advancement providing methods solving expanding practical applications.</p>

Язык: Английский

Quaternion modified conjugate gradient algorithm to solve Sylvester-type quaternion matrix equations with generalized coupled form as well as application DOI
Yifen Ke,

Xiaomin Cai,

Riwei Liao

и другие.

Applied Mathematics and Computation, Год журнала: 2025, Номер 495, С. 129330 - 129330

Опубликована: Янв. 30, 2025

Язык: Английский

Процитировано

1
An $ \eta $-Hermitian solution to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions DOI Creative Commons
Mahmoud Saad Mehany, Abdullah K. Alanazi

AIMS Mathematics, Год журнала: 2025, Номер 10(4), С. 7684 - 7705

Опубликована: Янв. 1, 2025

Язык: Английский

Процитировано

0
An Analysis to Some Systems of Matrix Equations with $${\phi }$$-Hermitian Solutions for Some Nonstandard Involution $${\phi }$$ Over the Real Quaternion Algebra DOI
Mahmoud Saad Mehany

Deleted Journal, Год журнала: 2025, Номер unknown

Опубликована: Янв. 23, 2025

Язык: Английский

Процитировано

0
Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications DOI Creative Commons
Abdur Rehman,

Muhammad Zia Ur Rahman,

Asim Ghaffar

и другие.

AIMS Mathematics, Год журнала: 2024, Номер 9(10), С. 26371 - 26402

Опубликована: Янв. 1, 2024

<p>In applied and computational mathematics, quaternions are fundamental in representing three-dimensional rotations. However, specific types of quaternionic linear matrix equations remain few explored. This study introduces new their necessary sufficient conditions for solvability. We employ a methodology involving lemmas ranks coefficient matrices to develop novel algorithm. algorithm is validated through numerical examples, showing its applications advanced fields. In control theory, these used analyzing systems, particularly spacecraft attitude aerospace engineering arms robotics. quantum computing, model gates transformations, which important algorithms error correction, contributing the development fault-tolerant computers. signal processing, enhance multidimensional filtering noise reduction, with color image processing radar analysis. extend our include cases $ \eta $-Hermitian i-Hermitian solutions. Our work represents an advancement providing methods solving expanding practical applications.</p>

Язык: Английский

Процитировано

0