Principles of local polynomial interpolation

Author(s):  
A. Schaum
Author(s):  
Francesco Dell’Accio ◽  
Filomena Di Tommaso ◽  
Najoua Siar ◽  
Marco Vianello

AbstractWe discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation.


CALCOLO ◽  
1994 ◽  
Vol 31 (3-4) ◽  
pp. 233-256 ◽  
Author(s):  
J. Hugger

2020 ◽  
Vol 5 (5) ◽  
pp. 550-553
Author(s):  
Victor Ayodele Ijaware ◽  
Adebayo T. Adeboye

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is a cooperative effort between NASA and Japan's Ministry of Economy Trade and Industry (METI), with the collaboration of scientific and industry organizations in both countries. The ASTER instrument provides a more robust remote sensing imaging capability when compared to the older Landsat Thematic Mapper. This paper deals with the accuracy assessment of elevation data obtained using ASTER from each of the eleven (11) selected extrapolation/interpolation algorithms: Inverse Distance Weighting, Natural Neighbor, Spline Regular, Spline Tension, Universal Kriging, Empirical Bayesian Kriging, Topo to Raster, global (trend surface), local polynomial, kernel interpolation with barriers and radial basis functions in Digital Elevation Model (DEM) surface creation. The data were compared with reference to ground control points of differential GPS measurements in the study area. The error statistics were generated between DGPS measurements and Extracted elevation data from each selected interpolation method. It was observed that Spline Regular Interpolation shown the best overall accuracy of ±11.520m when elevation data extracted from Inverse distance weighting, Natural Neighbour, Spline T, Topo to Raster, Universal Kriging, Empirical Bayesian kriging, Global polynomial interpolation (GPI), local polynomial interpolation (LPI), Radial basis function and Kernel interpolation of ±15.170, ±14.340, ±12.336, ±13.551, ±14.707, ±13.711, ±15.363, ±13.964, ±13.590 and ±15.376 respectively when compared with elevation values from GPS method. The study recommends capacity building in the form of workshop, training, and flexible integration of point elevation data to DEM.


2021 ◽  
Vol 20 ◽  
Author(s):  
I. G. Burova

The present paper is devoted to the application of local polynomial and non-polynomial interpolation splines of the third order of approximation for the numerical solution of the Volterra integral equation of the second kind. Computational schemes based on the use of the splines include the ability to calculate the integrals over the kernel multiplied by the basis function which are present in the computational methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra integral equations is also discussed. The results of the numerical experiments are presented.


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