A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method by Jutao Zhao, Pengfei Guo

“…The Jacobi–Davidson iteration method is very efficient in solving Hermitian eigenvalue problems. …”
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Some Aspects of Extended General Variational Inequalities by Muhammad Aslam Noor

“…The main motivation of this paper is to review some aspects of these variational inequalities including the iterative methods and sensitivity analysis. We expect that this paper may stimulate future research in this field along with novel applications.…”
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Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media by Piyush R. Mistry, Vikas H. Pradhan, Khyati R. Desai

“…An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.…”
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An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations by Hooman Darvishi, M. T. Darvishi

“…In order to solve systems of nonlinear equations, two novel iterative methods are presented. The successive over-relaxation method and the Chebyshev-like iterative methods to solve systems of nonlinear equations have combined to obtain the new algorithms. …”
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VIM for Solving the Pollution Problem of a System of Lakes by J. Biazar, M. Shahbala, H. Ebrahimi

“…This comparison reveals that the variational iteration method is easier to be implemented.…”
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Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects by Amir Naseem, M. A. Rehman, Thabet Abdeljawad

“…Several numerical examples have been solved which prove the better efficiency of these algorithms as compared to other well-known iterative methods of the same kind. Finally, the comparison of polynomiographs generated by other well-known iterative methods with our developed algorithms has been made which reflects their dynamical aspects.…”
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Optimization of Analytical Reconstruction Algorithms for Arbitrary CBCT Trajectory Using Deep Learning by Yuzhong Zhou, Linda-Sophie Schneider, Yipeng Sun, Andreas K. Maier

“…Although iterative methods are a common solution, they require substantial computational time and resources. …”
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Approximating fixed points of λ-firmly nonexpansive mappings in Banach spaces by Gang-Eun Kim

“…We study the convergence of the Ishikawa iteration methods to fixed points for the result of Smarzewski (1991). …”
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Bound-State Solution of s-Wave Klein-Gordon Equation for Woods-Saxon Potential by Eser Olğar, Haydar Mutaf

“…The bound-state solution of s-wave Klein-Gordon equation is calculated for Woods-Saxon potential by using the asymptotic iteration method (AIM). The energy eigenvalues and eigenfunctions are obtained for the required condition of bound-state solutions.…”
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On the Numerical Solution of Differential-Algebraic Equations with Hessenberg Index-3 by Melike Karta, Ercan Çelik

“…Numerical solution of differential-algebraic equations with Hessenberg index-3 is considered by variational iteration method. We applied this method to two examples, and solutions have been compared with those obtained by exact solutions.…”
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The Hybrid Steepest Descent Method for Split Variational Inclusion and Constrained Convex Minimization Problems by Jitsupa Deepho, Poom Kumam

“…We introduced an implicit and an explicit iteration method based on the hybrid steepest descent method for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem.…”
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An improved geometric algorithm for indoor localization by Junhua Yang, Yong Li, Wei Cheng

“…Comparing to trilateration, fingerprint, and maximum-likelihood method, the bilateral greed iteration method improves the localization accuracy and reduces complexity of localization process. …”
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Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System by Manuel F. Abad, Alicia Cordero, Juan R. Torregrosa

“…Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. …”
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Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion by Jun Wang, Li-xin Lu, Huan-xin Jiang, Yong Zhu

“…An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.…”
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New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations by İhsan Timuçin Dolapçı, Mehmet Şenol, Mehmet Pakdemirli

“…In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. …”
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Block Preconditioned SSOR Methods for -Matrices Linear Systems by Zhao-Nian Pu, Xue-Zhong Wang

“…We present a block preconditioner and consider block preconditioned SSOR iterative methods for solving linear system . When is an -matrix, the convergence and some comparison results of the spectral radius for our methods are given. …”
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Convergence of Viscosity Iteration Process for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings by Zhiming Cheng

“…We introduce a general iteration method for a finite family of generalized asymptotically quasi-nonexpansive mappings. …”
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Monte Carlo Alpha Iteration Algorithm for a Subcritical System Analysis by Hyung Jin Shim, Sang Hoon Jang, Soo Min Kang

“…The α-k iteration method which searches the fundamental mode alpha-eigenvalue via iterative updates of the fission source distribution has been successfully used for the Monte Carlo (MC) alpha-static calculations of supercritical systems. …”
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A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders by Young Ik Kim, Young Hee Geum

“…We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. …”
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Periodic and Antiperiodic Solutions for a Second-Order Hamiltonian System With Nonlinearity Depending on Derivative by Wenxiong Chen, Shibo Liu

“…We prove that there exists T0>0 such that, for any T<T0, the provided Hamiltonian system has a nontrivial T-periodic and T/2-antiperiodic solution via linking theorem and iteration method.…”
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