Solvability and algorithm for Sylvester-type quaternion matrix equations with potential applications

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(8), P. 19967 - 19996

Published: Jan. 1, 2024

<abstract><p>This article explores Sylvester quaternion matrix equations and potential applications, which are important in fields such as control theory, graphics, sensitivity analysis, three-dimensional rotations. Recognizing that the determination of solutions computational methods for these is evolving, our study contributes to area by establishing solvability conditions providing explicit solution formulations using generalized inverses. We also introduce an algorithm utilizes representations Moore-Penrose inverses improve efficiency. This validated with a numerical example, demonstrating its practical utility. Additionally, findings offer framework various existing results can be viewed specific instances, showing breadth applicability approach. Acknowledging challenges handling large systems, we propose future research focused on further improving algorithmic efficiency expanding applications diverse algebraic structures. Overall, establishes theoretical foundations necessary solving Sylvester-type introduces novel address their challenges, enhancing both understanding implementation complex equations.</p></abstract>

Language: Английский

Optimized design and analysis of cable-based parallel manipulators for enhanced subsea operations

Ocean Engineering, Journal Year: 2024, Volume and Issue: 297, P. 117012 - 117012

Published: Feb. 14, 2024

Language: Английский

Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(10), P. 26371 - 26402

Published: Jan. 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>

Language: Английский