A Critical Comparison of Some Methods for Interpolation of Scattered Data

Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave

“…It is easy to see that, asymptotically, c(n) ∼ 4n 3 for (7), c(n) ∼ 2n 3 for (8), and c(n) = O(n 2 log n) for (9). Nevertheless, as shown in Section 4, the matrix multiplication methods turn out to be competitive with the FFT-based method up to high degrees.…”

“…1). The Padua points (for n even) were introduced for the first time in [4, formula (9)] (in that formula there is a misprint, n − 1 has to be replaced by n + 1). Denoting by C n+1 the set of the n + 1 Chebyshev-Gauss-Lobatto points C n+1 = {z n j = cos((j − 1)π/n), j = 1, .…”

RBFs Meshless Method of Lines for the Numerical Solution of Time-Dependent Nonlinear Coupled Partial Differential Equations

“…Problem 3 Now we consider nonlinear coupled hyperbolic Equations (15). For the sake of comparison [6], we take 0.5,…”

“…Despite MQ's excellent performance, it contains a shape parameter c, and the accuracy of MQ is greatly affected by the choice of shape parameter c whose optimal value is still unknown. Franke [15] used the formula tance from each data point to its nearest neighbor. Hickernell and Hon [16] and Golberg et al [17] had successfully used the technique of cross-validation to obtain an optimal value of the shape parameter.…”

Smooth interpolation of large sets of scattered data

“…Since a number of methods are available for this important problem, a project was undertaken to test and compare as many methods as possible [4]. While the project included both global methods (meaning that S(x,y) is dependent on all data points regardless of their distance from (x,y)) and local methods (S(x,y) McLain [7] was the first to consider a family of inverse distance weighted least squares approximations.…”