The Quaternion Modified Gradient Based Iterative Algorithm of Quaternion Linear System

Authors: Li, Xinying, Song, Caiqin

Source: 2024 24th International Conference on Control, Automation and Systems (ICCAS) Control, Automation and Systems (ICCAS), 2024 24th International Conference on. :1643-1648 Oct, 2024

Relation: 2024 24th International Conference on Control, Automation and Systems (ICCAS)

QMGI algorithm for solving quaternion equation and its application in color image encryption

Authors: Li, Xinying^Aff1, Song, Caiqin^{Aff1, IDs1107502401920x_cor1}, Liu, Hongjun^Aff1

Source: Numerical Algorithms. 99(3):1429-1462

Quaternion modified conjugate gradient algorithm for η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}(-anti)-Hermitian solutions of generalized coupled Sylvester-type quaternion matrix equations

Authors: Cai, Xiaomin^Aff1, Zhuo, Wenxin^Aff1, Ke, Yifen^{Aff1, IDs11075025020900_cor1}, Liao, Riwei^{Aff2, IDs11075025020900_cor2}

Source: Numerical Algorithms. 101(4):2357-2379

New Gradient-Based Iterative-Like Algorithms for Solving a Class of Sylvester Tensor Equations

Authors: Huang, Zhengge^{Aff1, IDs42967025004853_cor1}

Source: Communications on Applied Mathematics and Computation. 8(3):1005-1049

Momentum acceleration-based gradient based iterative-like algorithms for the complex conjugate and transpose sylvester matrix equations

Authors: Huang, Zhengge^{Aff1, IDs11075025021849_cor1}

Source: Numerical Algorithms. 102(4):1981-2038

Applications of Mathematical Models in Engineering

Contributors: Dulf, Eva H., Muresan, Cristina I.

Subject Terms: fractional order IMC, first order plus dead-time processes, event-based implementation, numerical simulations, comparative closed loop results, nonlinear wave phenomen, RBF, local RBF-FD, stability, unmanned aerial vehicle (UAV), quaternion-based estimator, low-cost design, automatic optical inspection, kinetic theory, parallel robots, robust control, sliding mode control, basinI, basinII, mean pressure head, pressure head with different probabilities of occurrence, standard deviation of the pressure fluctuations, statistical modeling, USBR, desalination, humidification-dehumidification, waste heat recovery, mathematical model, yearly analysis, thermo-economics, multi-objective optimization, cruise altitude, fuel consumption, time to climb, Hermite-Simpson method, trajectory optimization, terminal residual analysis (TRA), m-σ terminal residual analysis (m-σ TRA), power transformer, stray losses, analytical methods, finite element method, gridshell structures, shape ratio, length ratio, regularity, particle swarm optimization, genetic algorithm, hybrid nanofluid, dual solutions, mixed convection, stagnation point, radiation, stability analysis, machine learning, eXterme Gradient Boosting, Computation Fluid Dynamics, blade vibration, unsteady aerodynamic model, active disturbance rejection control (ADRC), multiobjective optimization, time delay systems, tuning rules, soft robotics, fractional calculus, CACSD toolbox, operating point linearization, automatic uncertainty bound computation, Model-in-the-Loop simulation, hybrid simulation, ℋ∞ control, μ synthesis, DC-to-DC power converters, buck, boost, SEPIC, rainfall-runoff model, curve number, inferential statistics, 3D runoff difference model, model calibration, PAT model, modified affinity laws, hydraulic simulation tool, μ-synthesis, fractional-order control, swarm optimization, artificial bee colony optimization, CNC machine, mixed sensitivity, D–K iteration, Linear Matrix Inequality, biotechnology, fermentation process, batch bioreactors, modeling, control system design and synthesis, linear control, adaptive control, model reference adaptive control, control system realization, mixed-sensitivity, FO-PID, twin rotor aerodynamic system, Technology: general issues, History of engineering and technology

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Access URL: https://directory.doabooks.org/handle/20.500.12854/81012
https://mdpi.com/books/pdfview/book/5354

Attitude determination & control system design and implementation for a 6U CubeSat proximity operations mission

Authors: Franquiz, Francisco José, Franquiz, Francisco José

Subjects: Nanosatellites Attitude control systems., Space vehicles Control systems., Artificial satellites Design and construction., Véhicules spatiaux Systèmes de commande., Nanosatellites Attitude control systems

URL: https://commons.erau.edu/edt/266

A modified gradient‐based algorithm for solving extended Sylvester‐conjugate matrix equations.

Authors: Ramadan, Mohamed A., Bayoumi, Ahmed M. E.

Source: Asian Journal of Control; Jan2018, Vol. 20 Issue 1, p228-235, 8p

Subject Terms: Sylvester matrix equations, Algorithms, Iterative methods (Mathematics), Parameters (Statistics), Relaxation methods (Mathematics)

Riemannian gradient-based Zhang neural network method for linear discriminant analysis.

Authors: Wang, Yu-Hang, Xie, Zhuo-Cheng, Fu, Meng-Zhen, Ren, Huan

Source: AIMS Mathematics; 2026, Vol. 11 Issue 8, p1-21, 21p

Subject Terms: Classification algorithms, Artificial neural networks, Fisher discriminant analysis, Dimensional reduction algorithms, Human facial recognition software, Stability theory

Solvability, exact solution and momentum acceleration gradient-based iterative algorithm for general matrix equation AXB+CX¯D+EXTF+GX∗H=J and studying its applications in discrete-time antilinear systems and color image restoration.

Authors: Shirilord, Akbar, Dehghan, Mehdi

Source: Numerical Algorithms; Apr2026, Vol. 101 Issue 4, p2505-2566, 62p

Subject Terms: Iterative methods (Mathematics), Momentum (Mechanics), Discrete-time systems, Matrix multiplications, Matrices (Mathematics), Numerical analysis

QGI Algorithm for Solving Quaternion Equation Arising in Image Encryption.

Authors: Li, Xinying, Song, Caiqin

Source: Mathematical Methods in the Applied Sciences; Aug2025, Vol. 48 Issue 12, p12514-12527, 14p

Subject Terms: Quaternions, Image encryption, Quaternion functions, Least squares, Data encryption

QRGI Algorithm for Solving Quaternion Equation and Its Application.

Authors: Li, Xinying, Song, Caiqin

Source: Optimal Control - Applications & Methods; Sep2025, Vol. 46 Issue 5, p2045-2066, 22p

Subject Terms: Quaternions, Signal processing, Least squares, Empirical research, Image processing, Time complexity, Image encryption

Gradient-Based Recursive Parameter Estimation Methods for a Class of Time-Varying Systems from Noisy Observations.

Authors: Xu, Ning, Liu, Qinyao, Ding, Feng

Source: Circuits, Systems & Signal Processing; Nov2024, Vol. 43 Issue 11, p7089-7116, 28p

Subject Terms: Autoregressive models, Time-varying systems, Parameter estimation, Parameter identification, Algorithms

Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C.

Authors: Wang, Huiling, Wu, Nian-Ci, Nie, Yufeng

Source: AIMS Mathematics; 2024, Vol. 9 Issue 12, p1-19, 19p

Subject Terms: Sylvester matrix equations, Algorithms

An alternative kernel adaptive filtering algorithm for quaternion-valued data

Authors: Ogunfunmi, Tokunbo, Paul, Thomas

Source: Proceedings of The 2012 Asia Pacific Signal and Information Processing Association Annual Summit and Conference Signal & Information Processing Association Annual Summit and Conference (APSIPA ASC), 2012 Asia-Pacific. :1-5 Dec, 2012

Relation: 2012 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC)

Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation.

Authors: Xie, Mengyan, Wang, Qing-Wen, Chen, Jie

Source: Numerical Algorithms; Feb2026, Vol. 101 Issue 2, p1023-1047, 25p

Subject Terms: Sylvester matrix equations, Artificial neural networks, Online algorithms, Numerical analysis, Mathematical proofs

Quaternion-Valued Stochastic Gradient-Based Adaptive IIR Filtering.

Authors: Took, Clive Cheong, Mandic, Danilo P.

Source: IEEE Transactions on Signal Processing; Jul2010, Vol. 58 Issue 7, p3895-3901, 7p

Subject Terms: Quaternion functions, Quaternions, Algorithms, Impulse response, Signal processing

Solving a system of complex matrix equations using a gradient-based method and its application in image restoration.

Authors: Shirilord, Akbar, Dehghan, Mehdi

Source: Numerical Algorithms; Apr2025, Vol. 98 Issue 4, p1849-1896, 48p

Subject Terms: Systems theory, Complex matrices, Computational mathematics, Image reconstruction, Constrained optimization

A relaxed gradient based iterative algorithm of the generalized Sylvester-conjugate matrix equation over centro-symmetric and centro-Hermitian matrices.

Authors: El-Shazly, Naglaa M, Ramadan, Mohamed A, El-Sharway, Marwa H

Source: Journal of Vibration & Control; Oct2023, Vol. 29 Issue 19/20, p4396-4412, 17p

Subject Terms: Hermitian forms, Matrices (Mathematics), Sylvester matrix equations, Equations

Training-Free Few-Shot Image Classification via Kernel Density Estimation with CLIP Embeddings.

Authors: Pacheco dos Santos Lima Junior, Marcos Sergio, Ortiz-de-Lazcano-Lobato, Juan Miguel, López-Rubio, Ezequiel

Source: Mathematics (2227-7390); Nov2025, Vol. 13 Issue 22, p3615, 28p

Subject Terms: Image recognition (Computer vision), Probability density function, Machine learning, Dimensional reduction algorithms