Akima Spline Interpolation

Function: - Akima Spline Interpolation 5

It is an example of a difficult function. Argument has very fast oscillations near to zero. When it is multiplied with then the amplitude will start to reduce as we are approach zero. If we plot a small number of nodes, we will get an incorrect function. The only solution is to fit enough nodes. In this case we have used 100 nodes which is insufficient. Therefore we have increased the number of fitted nodes to 500.

Graph 26. Function: exp(-x)*sin(2*_pi/x) - Akima Spline Interpolation. If we are going towards zero the function should become periodic with increasing amplitude. We can see that this Akima, with 100 fitted nodes, is absolutely insufficient compared to Graph 27. where we have used 500 nodes.

Graph 27. Function: exp(-x)*sin(2*_pi/x) - Akima Spline Interpolation. If we are falling to zero then the amplitude will rise but we can see that the Akima has not succeeded in improving. The graph of the curve has been constructed at an interval from 0 to 1.5 with 500 nodes. If we used more fitted nodes then we will achieve better results. It is a question of whether we will have enough nodes as any further increase will produce an improvement but maybe not enough.

Graph 28. Magnified Graph 27. Function exp(-x)*sin(2*_pi/x) - Akima Spline Interpolation. The third minimum produces the largest mistake. The only solution is to increase the fitted nodes.