AN IDENTITY ON SYMMETRIC POLYNOMIALS by Đặng Tuấn Hiệp, Lê Văn Vĩnh

“…In order to obtain this identity, we use the interpolation theory, in particular, the Lagrange interpolation formula. …”
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Rainfall Variability, Drought Characterization, and Efficacy of Rainfall Data Reconstruction: Case of Eastern Kenya by M. Oscar Kisaka, M. Mucheru-Muna, F. K. Ngetich, J. N. Mugwe, D. Mugendi, F. Mairura

“…Spline, Kriging, and inverse distance weighting interpolation techniques were assessed using daily rainfall data and digital elevation model using ArcGIS. …”
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Research on Improved Ray Casting Algorithm and Its Application in Three-Dimensional Reconstruction by ZheShu Jia, DeYun Chen, Bo Wang

“…This method first classifies CT data, assigns corresponding color values and opacity transfer functions to different types of data, and then uses inverse distance-weighted interpolation (IDWI) sampling to replace the trilinear interpolation sampling method for the voxel where the sampling point is located to accelerate the interpolation operation. …”
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Analysis and Simulation of Polishing Robot Operation Trajectory Planning by Xinhong Zeng, Yongxiang Wang

“…We then propose a novel approach by implementing both fifth-degree polynomial and quintic B-spline interpolation algorithms for planning the robot’s spatial spiral arc trajectory, which is a key contribution of this work. …”
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Comparison of the stability of discontinuous Galerkin and finite-difference methods by Raimondas Čiegis, Remigijus Čiegis, Olga Suboč

“…It is proved that interpolation error accumulates during computations while projection error has much better stability properties. …”
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Ambient Ozone Exposure in Czech Forests: A GIS-Based Approach to Spatial Distribution Assessment by I. Hůnová, J. Horálek, M. Schreiberová, M. Zapletal

“…Our results indicate that the optimal interpolation approach is linear regression of O3 data and altitude with subsequent interpolation of its residuals by ordinary kriging. …”
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Atomic decompositions of Lorentz martingale spaces and applications by Jiao Yong, Peng Lihua, Liu Peide

“…Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.…”
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Runoff Simulation Study of Ganjiang River Basin Based on Distributed Time-varying Gain Hydrological Model and CN05.1 Precipitation Data by ZHONG Qi, FU Xiaolei, JIANG Xiaolei, ZHANG Yuchen, HU Leyi, ZHANG Liping

“…A hydrological model is an important tool for simulating runoff,with precipitation being a key factor in the hydrological cycle.The choice of model and the quality of precipitation data are crucial for accurately simulating runoff in river basins.This paper focuses on the Ganjiang River Basin and analyzes the reliability of CN05.1 precipitation data by comparing it with station linear interpolated precipitation data. Additionally,the paper evaluates the applicability of the distributed time-variant gain hydrological model (DTVGM) and CN05.1 precipitation data in simulating runoff in the Ganjiang River Basin.The results show that:① CN05.1 precipitation and station interpolated precipitation exhibit similar variation patterns over multiple years,with a high spatial distribution correlation and a mean correlation coefficient (R) of 0.90.The correlation between CN05.1 daily precipitation and interpolated daily precipitation is also high,with a root mean square error (RMSE) of less than or equal to 7.52 mm and an R value greater than or equal to 0.81.② Using CN05.1 precipitation and station interpolated precipitation data,the flow of six hydrological stations,including Xintian,in the Ganjiang River Basin is simulated from 1961 to 2009.The simulated flow generally exceeds the measured flow during high flow periods,indicating that the model overestimates the simulation of large flows.③ The accuracy of runoff simulation based on CN05.1 precipitation is high, whether for daily or monthly runoff, with better performance in simulating monthly runoff compared to daily runoff.Therefore,the DTVGM model and CN05.1 precipitation data are highly applicable for runoff simulation in the Ganjiang River Basin.…”
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On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules by Shuhuang Xiang, Guo He, Haiyong Wang

“…Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver’s algorithms, this paper presents fast and stable interpolating integration algorithms, by using the coefficients and modified moments, for Clenshaw-Curtis, Fejér’s first- and second-type rules for Jacobi weights or Jacobi weights multiplied by a logarithmic function. …”
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Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application by Yuanpeng Zhu, Xuli Han, Shengjun Liu

“…The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a C1 positivity- or monotonicity- preserving interpolation spline. …”
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A Trajectory Planning Method for Optimal Energy Consumption of the Hydraulic Excavator by Zhang Yunyue, Sun Zhiyi, Sun Qianlai, Wang Yin, Yang Jiangtao

“…In order to reduce the movement energy consumption of the hydraulic excavator and realize the reasonable and effective operation of each joint, a joint interpolation method based on a T-type velocity curve is proposed to realize the optimal energy consumption trajectory planning of the hydraulic excavator. …”
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Numerical Compensation Method for Measuring Error of Tooth Profile of ZC1 Worm on Shaft Section by Zhiqiang Zhu, Jie Tang, Zhaoyao Shi

“…Therefore，the tooth profile theoretical contact points close to the actual contact points are solved by subdivision method，Newton interpolation method and cubic spline interpolation method，and the compensated tooth profile deviation can be obtained. …”
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Enhancing environmental monitoring of harmful algal blooms with ConvLSTM image prediction by Sung Jae Kim, Yongbok Cho

“…Using 3D universal kriging, the study interpolates missing HAB concentration values, transforming geospatial point data into spatially continuous grid images that serve as the foundation for predictive modeling. …”
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Schwarzschild-Levi-Civita black hole by S. Habib Mazharimousavi

“…Inspired by the geometry of the Ernst black hole which interpolates the static spherically symmetric Schwarzschild black hole and the static axially symmetric magnetic Melvin spacetime, in this paper, we aim to present a solution to Einstein's field equation in vacuum to interpolate the Schwarzschild black hole and the Levi-Civita spacetime. …”
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Pengembangan Metode Interpolasi Splin Kubik Terapit dan Aplikasinya pada Masalah Pelacakan Trajektori Objek by Elvathna Syafwan, Mahdhivan Syafwan, Shandy Tresnawati

“…Abstrract Cubic spline interpolation is a very popular curve fitting method since it is easy to implement and produces a smooth curve. …”
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HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation by Shu-Li Mei, De-Hai Zhu

“…Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. …”
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Parenthèses et ruptures énonciatives en langue des signes française by Annie Risler

“…When applied to oral speech, the concept of parenthesis refers to a particular type of interpolated phrase, bounded on the left and on the right, and determined by prosodic, syntactic and discursive characteristics. …”
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The effect of resizing on the natural appearance of scintigraphic images: an image similarity analysis by Siraj Ghassel, Amir Jabbarpour, Jochen Lang, Eric Moulton, Eric Moulton, Ran Klein, Ran Klein, Ran Klein, Ran Klein

“…Naïve upsampling and downsampling with linear interpolation were compared against alternative methods based on the preservation of Poisson count statistics and principles of nuclear scintigraphic imaging; namely, linear interpolation with a Poisson resampling correction (upsampling) and a sliding window summation method (downsampling). …”
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Improving the Accuracy of PV Yield Calculation by Exploitation of Real Weather Data by Andreas Schneider, Matthias Buschmann, Jorge Rabanal-Arabach, Julia Chochollek, Thomas Nierhoff

“…Since data from weather stations is not available for most locations world-wide this data is calculated by using modern interpolation methods. Beside this, simulation software typically uses historical weather data. …”
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Methods Research on Correction for Intracranial Metal Artifacts Based on Prior Image Utilization by Zonggui CHEN, Ningning WEI, Zhoufan LI, Guihong PAN, Minjiang HUANG

“…Two senior doctors subjectively scored this algorithm higher than the linear interpolation and ADN algorithms for removing CT metal artifacts. …”
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