Let , and assume the interpolation is a cubic curve. Use equations (3) and (5) to compute the and , and then set up the system of linear equations, equation (1). The separate chord lengths are given by, , , and the total chord length is . Thus, , , , . So . Thus Spline interpolation uses all of the available data to construct a cubic between each pair of points that has is continuous with continuous first and second derivatives. Lagrange interpolation simply interpolates with a cubic polynomial the two points below the region and the two points above the region.
Let’s use MatLab’s interp1 function to construct linear and cubic spline approximants to the function y(x) = exp(x)*sin(5x) N=16 as before. See SplineL10.m yi = Interp1(x,y,xi,’spline’) interpolates a cubic spline from data (x,y) at the points xi The cubic spline results look good, but Chebyshev interpolation with N=16 gives a much
SAGA-GIS Tool Library Documentation (v3.0.0) Tools A-Z Contents Library Spline Interpolation. ... Cubic Spline Approximation;