A Lagrange Interpolation Method by Trivariate Cubic C 1 Splines of Low Locality

2011 ◽  
pp. 231-248
Author(s):  
G. Nürnberger ◽  
G. Schneider
Keyword(s):  
Lagrange Interpolation ◽  
Interpolation Method

scholarly journals Comparative study of the implementation of the Lagrange interpolation algorithm on GPU and CPU using CUDA to compute the density of a material at different temperatures

2021 ◽  
Vol 119 ◽  
pp. 07002
Author(s):  
Youness Rtal ◽  
Abdelkader Hadjoudja
Keyword(s):  
Parallel Computing ◽  
Graphics Processing Units ◽  
Lagrange Interpolation ◽  
Polynomial Interpolation ◽  
Programming Model ◽  
Interpolation Method ◽  
Processing Unit ◽  
Central Processing ◽  
Computational Performance ◽  
Different Temperatures

Graphics Processing Units (GPUs) are microprocessors attached to graphics cards, which are dedicated to the operation of displaying and manipulating graphics data. Currently, such graphics cards (GPUs) occupy all modern graphics cards. In a few years, these microprocessors have become potent tools for massively parallel computing. Such processors are practical instruments that serve in developing several fields like image processing, video and audio encoding and decoding, the resolution of a physical system with one or more unknowns. Their advantages: faster processing and consumption of less energy than the power of the central processing unit (CPU). In this paper, we will define and implement the Lagrange polynomial interpolation method on GPU and CPU to calculate the sodium density at different temperatures Ti using the NVIDIA CUDA C parallel programming model. It can increase computational performance by harnessing the power of the GPU. The objective of this study is to compare the performance of the implementation of the Lagrange interpolation method on CPU and GPU processors and to deduce the efficiency of the use of GPUs for parallel computing.

Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Fakhrodin Mohammadi
Keyword(s):  
Approximate Solution ◽  
Finite Number ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Treatment ◽  
Nonlinear Integral Equations

This paper deals with the approximate solution of nonlinear stochastic Itô–Volterra integral equations (NSIVIE). First, the solution domain of these nonlinear integral equations is divided into a finite number of subintervals. Then, the Chebyshev–Gauss–Radau points along with the Lagrange interpolation method are employed to get approximate solution of NSIVIE in each subinterval. The method enjoys the advantage of providing the approximate solutions in the entire domain accurately. The convergence analysis of the numerical method is also provided. Some illustrative examples are given to elucidate the efficiency and applicability of the proposed method.

Interpolation Method Research and Precision Analysis of GPS Satellite Position

2018 ◽  
Vol 6 (3) ◽  
pp. 277-288
Author(s):  
Jianmin Wang ◽  
Yabo Li ◽  
Huizhong Zhu ◽  
Tianming Ma
Keyword(s):  
Lagrange Interpolation ◽  
Hermite Interpolation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Newton Interpolation ◽  
Cubic Spline Interpolation ◽  
Satellite Position ◽  
Precise Ephemeris ◽  
Better Than

Abstract According to the precise ephemeris has only provided satellite position that is discrete not any time, so propose that make use of interpolation method to calculate satellite position at any time. The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation, Newton interpolation, Hermite interpolation, Cubic spline interpolation method, Chebyshev fitting method respectively, which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst, the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore, Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.

scholarly journals Interval Recognition Algorithm of the Pavement Surface Condition Based on Lagrange Interpolation Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Ren He ◽  
Liwei Zhang
Keyword(s):  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Estimation Error ◽  
Surface Condition ◽  
Recognition Algorithm ◽  
Identification Algorithm ◽  
Pavement Surface ◽  
Road Condition ◽  
Road Friction ◽  
Road Friction Coefficient

The accurate recognition of road condition is one of the important factors that influence vehicle safety performance. This paper comes up with an original mathematical method of an interval recognition algorithm of the pavement surface condition based on Lagrange interpolation. The ordinate of the peak point is solved by the Lagrange interpolation method, and the pavement surface condition is deduced by the interval identification algorithm. The simulation results from six typical roads and the varied pavement surface show that besides the cobblestone pavement which is not common in the daily road, the estimation error of the initial tire-road friction coefficient by the Lagrange interpolation method is less than 2%, the pavement surface condition can be identified by interval recognition algorithm quickly and accurately, and the response time is less than 0.2 seconds.

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