Convergence Region of Newton Iterative Power Flow Method: Numerical Studies by Jiao-Jiao Deng, Hsiao-Dong Chiang

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Some properties of the basins of attraction of the Newton’s method for simple nonlinear geodetic systems by Winnicki Ireneusz, Kroszczynski Krzysztof, Kiliszek Damian

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An iterative method based on the average quadrature formula by Tusar Singh, Dwiti Behera, Shno Othman Ahmed, Rostam Saeed

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Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation by Chacha Stephen Chacha

“…This article explores the application of exact line search and successive over-relaxation techniques to enhance the convergence of Newton method in solving the Yang-Baxter matrix equation for nontrivial numerical solutions. …”
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Improved Newton Iterative Algorithm for Fractal Art Graphic Design by Huijuan Chen, Xintao Zheng

“…Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. …”
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Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion by Henryk Leszczyński, Monika Wrzosek

“…The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.…”
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A Unified Kantorovich-type Convergence Analysis of Newton-like Methods for Solving Generalized Equations under the Aubin Property by Samundra Regmi, Ioannis K. Argyros, Santhosh George, Jefferey Warden

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Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity by Plamena I. Marcheva, Stoil I. Ivanov

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Artificial Bee Colony and Newton Algorithm for Forward Position Solution of Parallel Mechanism by Ping Li, Siyang Peng, Linxian Che, Li Du, Junkun Hong

“…By an organic combination of the intelligent optimization algorithm and the numerical iteration method， a general algorithm called hybrid artificial bee colony and Newton iteration （HABC-Newton） algorithm for solving the forward positions of parallel mechanism is constructed. …”
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A Newton-type method and its application by V. Antony Vijesh, P. V. Subrahmanyam

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On Traub–Steffensen-Type Iteration Schemes With and Without Memory: Fractal Analysis Using Basins of Attraction by Moin-ud-Din Junjua, Shahid Abdullah, Munish Kansal, Shabbir Ahmad

“…Steffensen’s method overcomes the drawback of the derivative evaluation of Newton’s scheme, but it has, in general, smaller sets of initial guesses that converge to the desired root. …”
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Improved FastICA algorithm for data optimization processing in intrusion detection by Ye DU, dan ZHANGYa, hong LIMei, wei ZHANGDa

“…The weighted correlation coefficient was adopted in the phase of albinism processing to reduce information loss, and the Newton's iterative method was improved for third-order convergence. …”
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A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method by M. Bahi, M. Beggas, N. Nesba, A. Imtiaz

“…In this article, we apply three numerical methods to study the L∞-convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand side. …”
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Jacobian-Free Newton Krylov Methods for Steady and Transient Neutron Transport Models by ZHANG Yangyi, ZHANG Tiancheng, ZHOU Xiafeng

“…Numerical results also show that the parallel solver called comeSn_JFNK can achieve an acceleration of over 10 times for KAIST-3A benchmark problems and approximately 30 times for C5G7-TD2 cases compared to the original parallel comeSn code using the traditional source iteration/power iteration methods. These solutions indicate that the JFNK methods offer significant acceleration for solving both steady-state and transient SN neutron transport models compared to traditional source iteration/power iteration methods. …”

An innovative and efficient implementation of matrix-free Newton krylov method for neutronics/thermal-hydraulics coupling simulation by Peijun Li, Chen Hao, Ning Xu, Yanling Zhu, Yizhen Wang, Zhigang Zhang

“…In this work, an efficient and robustness coupling method using power density as the coupling parameter, Matrix-Free Newton Krylov (MFNK) method, is successfully developed and innovatively implemented in HNET for high-fidelity N/TH coupling simulation. …”
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Power flow calculation of electricity-gas integrated energy systems using an improved Newton-Raphson method by WENG Geping, REN Jiaorong, LI Qi, WENG Bingyu, CAI Zhenhua, HAN Yinfeng, LU Shuai

“…To address the difficulty in convergence encountered in power flow calculations of integrated electricity-gas energy systems using the traditional Newton-Raphson method for state evaluation and safety checks， this paper proposes a power flow calculation method based on an improved continuous Newton method. …”
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Memoryless quasi-Newton-type methods via some weak secant relations for large-scale unconstrained optimization by Keat Hee Lim, Wah June Leong

“…Abstract This article presents two variants of memoryless quasi-Newton methods with backtracking line search for large-scale unconstrained minimization. …”
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A Hybrid Approach Incorporating WSO-HO and the Newton-Raphson Method to Enhancing Photovoltaic Solar Model Parameters Optimisation by Jeridi Ahmed, Moulahi Mohamed Hedi, Khaterchi Hechmi, Zaafouri Abderrahmen

“…This study introduces a novel hybrid approach, WSO-HO, which integrates the strengths of the war strategy optimization (WSO) and Hippopotamus Optimization (HO) algorithms, enhanced by the Newton-Raphson (NR) method, to achieve precise parameter estimation for PV models. …”
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Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots by Fiza Zafar, Nawab Hussain, Zirwah Fatimah, Athar Kharal

“…We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. …”
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An Improved Reduced-Dimension Robust Capon Beamforming Method Using Krylov Subspace Techniques by Xiaolin Wang, Xihai Jiang, Yaowu Chen

“…The diagonal loading level of RDRCB is known to become invalid if the initial value of the Newton iteration method is incorrect and the Hessel matrix is non-positive definite. …”
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