A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis by Xingwu Zhang, Xuefeng Chen, Zhibo Yang, Bing Li, Zhengjia He

“…Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. …”
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Integrating the Finite Element Method with a Data-Driven Approach for Dam Displacement Prediction by Chenfei Shao, Chongshi Gu, Zhenzhu Meng, Yating Hu

“…Moreover, with a Lagrange polynomial interpolation, we can obtain the distribution field of elastic modulus, rather than gaining one value for the whole dam in previous studies. …”
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Evaluating the stability and efficacy of fractal-fractional models in reproductive cancer apoptosis with ABT-737 by Kottakkaran Sooppy Nisar, M. Sivashankar, S. Sabarinathan, C. Ravichandran, V. Sivaramakrishnan

“…The numerical schemes utilize the basic concepts of fractional calculus and Lagrange polynomial interpolation. We generate simulated graphical representations of these models for a variety of fractional-order values. …”
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Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives by Seyfeddine Moualkia, Yang Liu, Jinde Cao

“…The numerical simulations are done based on the Euler–Maruyama method and with the help of Lagrange polynomial interpolation, enabling the authors to extract meaningful results from the model. …”
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Excavating trajectory planning of electric shovel based on dynamic excavating volume prediction by Juan Wu, Rui Liu, Baoguo Lin

“…Then, the trajectory model of the dipper tooth tip is established by using the 6th polynomial interpolation method, and the minimum excavation energy consumption per unit volume is taken as the optimization objective, and the whale optimization algorithm is used to plan the excavation trajectories for four kinds of complex stacking surfaces (concave, convex, convex–concave and stepped stacking surfaces). …”
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Reentry Trajectory Optimization for a Hypersonic Vehicle Based on an Improved Adaptive Fireworks Algorithm by Xing Wei, Lei Liu, Yongji Wang, Ye Yang

“…First, via the Chebyshev polynomial interpolation, the trajectory optimization problem with infinite dimensions is transformed to a nonlinear programming problem (NLP) with finite dimension, and the scope of angle of attack (AOA) is obtained by path constraints to reduce the difficulty of the optimization. …”
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Anomaly detection in multidimensional time series for water injection pump operations based on LSTMA-AE and mechanism constraints by Mei Wang, Xinyuan Zhu, Guangyue Zhou, Kewen Li, Qingshan Wu, Wankai Fan

“…Experimental results demonstrate that this approach significantly outperforms methods such as polynomial interpolation, random forest, and LSTM-AE in terms of anomaly detection accuracy on field datasets from oilfields, accompanied by a notably lower false alarm rate.…”
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LOCAL INTERPOLATION AND APPROXIMATION IN TASKS OF HEURISTIC SYNTHESIS OF DIGITAL FILTER by V. N. Isakov, P. I. Timoshenko

“…Digital differentiators based on local polynomial interpolation, digital integrators based on local polynomial and spline interpolation and digital filters with a U-shaped amplitude-frequency characteristic based on polynomial OLS approximation are obtained. …”
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Equiconvergence of some sequences of rational functions by M. A. Bokhari, A. Sharma

“…The phenomenon of equiconvergence was first observed by Walsh for two sequences of polynomial interpolants to a class of functions. Here we obtain analogues of Yuanren's results for Walsh equiconvergence using rational functions as in Saff and Sharma. …”
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Matrix Transformations and Disk of Convergence in Interpolation Processes by Chikkanna R. Selvaraj, Suguna Selvaraj

“…Walsh proved that the difference of the Lagrange polynomial interpolant of 𝑓(𝑧)∈𝐴𝜌 and the partial sum of the Taylor polynomial of 𝑓 converges to zero on a larger set than the domain of definition of 𝑓. …”
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