Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations by Ling Li, Yongxian Li

“…The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. …”
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Dynamics of the rational difference equations by Burak Oğul

“…Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. …”
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Design scheme of physical layer security for intelligent reflecting surface-assisted MISO communication system by Xiaorong JING, Zhenyuan SONG, Wei GAO, Weijia LEI, Qianbin CHEN

“…Intelligent reflecting surface (IRS) improves the physical layer security of the communication systems by adjusting the phases of the reflecting units.A scheme of physical layer security design based on alternative iteration was proposed for IRS-assisted multiple input single output (MISO) communication system.Firstly, aiming at maximizing the secrecy rate, a non-convex objective function with non-convex constraints was constructed.Secondly, the Dinkelbach algorithm and Riemannian manifold optimization algorithm were adopted to transform the non-convex problem into a series of solvable sub-problems.Finally, the alternate iteration method was used to achieve the optimization design of transmit beamforming and IRS phase shift matrix.The simulation results show that, compared with the several existing schemes, the proposed scheme can achieve a better tradeoff between computational complexity and system security rate.…”
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GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography by Martin Schweiger

“…The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. …”
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Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering by M. A. Rehman, Amir Naseem, Thabet Abdeljawad

“…These problems also include some real-life applications associated with the chemical and civil engineering such as adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia, the van der Wall’s equation, and the open channel flow problem whose numerical results prove the better efficiency of these methods as compared to other well-known existing iterative methods of the same kind.…”
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Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation by Javad Alinejad, Sina Samarbakhsh

“…The obtained equations, including nonlinear equation for the velocity field 𝑓 and differential equation by variable coefficient for the temperature field 𝜃, are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. The effect of various values of Prandtl number, Eckert number and nonlinear stretching parameter are studied. …”
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Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context by Yousuf Alkhezi, Ahmad Shafee

“…This study intends to investigate methods such as the Aboodh transform iteration method and the Aboodh residual power series method, specifically for addressing the Jaulent–Miodek system of partial differential equations. …”
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A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation by Abdon Atangana, S. C. Oukouomi Noutchie

“…The modified equation is solved via the technique of green function and the variational iteration method.…”
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A Novel Approach with Comparative Computational Simulation of Analytical Solutions of Fractional Order Volterra Type Integral Equations by Javed Iqbal, Khurram Shabbir, Liliana Guran, Homan Emadifer

“…The main purpose of this article is to reconsider the theory of variational iteration method and embed it with Laplace transform to construct the conjoined technique variational iteration Laplace transform method. …”
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ENGAGEMENT MODEL OF DOWNHOLE MOTOR AND APPLICATION by KUANG YuChun, ZHANG Cong, WU LongMei, DONG ZongZheng, REN HaiTao

“…Through the balance theory of contact force system and the iteration method,the center trace of rotor and the normal interference were obtained. …”
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Bias-free policy evaluation in the discrete-time adaptive linear quadratic optimal control in the presence of stochastic disturbances by Vina Putri Virgiani, Natsuki Ishigaki, Shiro Masuda

“…The existing deterministic policy iteration method realizes an adaptive LQ optimal regulator. …”
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Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities by L. C. Ceng, A. Latif, C. F. Wen, A. E. Al-Mazrooei

“…We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions, and the solution set of general system of variational inequalities (GSVI), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. …”
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Influence of Varnish on Bearing Performance and Vibration of Rotating Machinery by Chu Zhang, Jian-Gang Yang, Shi Liu, Qing-Shui Gao, Yi Yang

“…Pressure and temperature distribution were solved on the basis of the Reynolds equation by the iteration method simultaneously. It is found that bearing performance is changed by the step flow effect at the leading edge of the varnish. …”
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ACCELERATED ITERATIVE RECONSTRUCTION OF PHANTOM «ROZI» BY OS-SART METHOD USING ORDERED SUBSET PROJECTIONS by S. A. Zolotarev, M. M. Mieteeg, A. N. Al-Nadfa

“…The desire to increase the convergence rate of the iterative methods led to the use of ordered subsets of projections for both the maximum likelihood method of EM (OS-EM) and for the algebraic reconstruction method with simultaneous iterations of SART (OS-SART). …”
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Scatter and Blurring Compensation in Inhomogeneous Media Using a Postprocessing Method by Yan Yan, Gengsheng L. Zeng

“…This method also offers an alternative to compensate for scatter and blurring in a more time efficient manner compared to the popular iterative methods. The execution time for this efficient postprocessing method is only a few minutes, which is within the clinically acceptable range.…”
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Influence of Roughness on Isothermal Elastohydrodynamic Lubrication of Roller Enveloped Worm Drive by Yan Qi, Honghui Liao, Xudong Wang, Zaixin Liu, Jinkuan Li

“…According to the elastohydrodynamic lubrication theory， the Newton iteration method is used in Matlab. The Newton-Raphson method is used to solve its numerical calculation， the conjugate teeth of the new transmission pair are studied， and the analysis of the line contact between the conjugate teeth is completed. …”
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NONLINEAR VIBRATION RESEARCH OF STRIP STEEL WITH CONSIDERATION OF TORSIONAL VIBRATION OF MAIN DRIVE SYSTEM OF ROLLING MILL by GAO ChongYi, DU GuoJun, LI Rui, LIU XiaoMan

“…Then, the nonlinear vibration differential equations of the coupled model were derived with Hamilton’s principle. The modified iteration method and the Kantorovich averaging method were used to solve the differential equations. …”
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Loopback matching algorithm with support set protection by Shu-juan TIAN, Xiao-ping FAN, Ting-rui PEI, Shu YANG, Zhe-tao LI

“…There was a drawback of deleting right support elements in some greedy iterative reconstruction algorithms.To resolve this problem,loopback matching algorithm with support set protection (LM-P) was proposed.First,LM-P ini-tialized elements of non-protected support set based on minimum residual inner product.Second,it computed the projec-tions of observations on the observation sub-matrix corresponding to non-protected support set elements.Then,an ele-ment in non-protected support set with the largest projection was added to the protected support set.An alternative multi-plicative iteration method was employed to obtain the whole protected support set.As to reconstruct a sparse signal whose nonzero elements are normally distributed and the signal sparsity is less than half the number of measurements,experimental results show that the reconstruction accuracy of LM-P algorithm exceeds 86%.For sparse signals with small noise,the reconstruction accuracy of LM-P can maintain over 99 %.Compared with OMP,CoSaMP,SP and GPA algo-rithms,LM-P's observations are smaller.LM-P also has good performance for image reconstruction.greedy iteration;support set;sparse signal;LM-P…”
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Application of Gap Metric to LADRC Design in Multilinear Model of SDR by Hongfu Wang, Qinghua Zeng, An Wang, Zongyu Zhang

“…In this paper, under the LADRC frame, the gas generator system’s closed-loop stability of the SDR was analyzed and the range of compensation factors had been calculated, and then, the “gap factor” was introduced and the “cross-iteration” method was used to quickly map out the “compensation factor” in the multilinear model controller based on the variation of the zero-point position of the system and the gap metric between adjacent set points. …”
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An efficient technique to study of time fractional Whitham–Broer–Kaup equations by Nishant Bhatnagar, Kanak Modi, Lokesh Kumar Yadav, Ravi Shanker Dubey

“…Comparative numerical analyses are conducted with outcomes from the Adomian decomposition method (ADM), variational iteration method (VIM), and optimal homotopy asymptotic method (OHAM), demonstrating the superior accuracy of the proposed method. …”
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