Cubic Spline Interpolation

Function: - Cubic Spline Interpolation 7

It is an example of a very difficult function. Argument has a very fast oscillation near to zero. When it is multiplied by then, if we a re moving to zero, the amplitude will start to diminish. If we use a small number of nodes we will obtain an incorrect function. The only solution is that the user adds more nodes. In our case we have first used 100 nodes and than we have increased the number to 500 nodes as 100 nodes was not sufficient.

Graph16. Function created by the Cubic Spline interpolation with 100 nodes (green curve). These 100 nodes are insufficient for interpolation. There are large differences between linear and Cubic Spline interpolations. The Cubic Spline has poor interpolation completely missing some oscillations at the start of the curve.

Graph16a. Function same as Graph 16. with applied Cubic Spline interpolation with 500 fitted nodes. We can see that the interpolation is periodic but there is problem to reach the amplitude. Cubic Spline (green curve) rises above the linear interpolation (red curve).

Graph17. Function is made by Cubic Spline with 500 fitted nodes (green curve). The maximums should be increasing from left to right. The second maximum is lower than the first maximum on the left side of the graph. Please note that the linear interpolation is much worse than the Cubic Spline.