Hermite Spline Interpolation

Function: - Hermite Spline Interpolation 1

This is a very useful function for testing interpolation. The function amplitude is always constant with a value 1.0 and with a constant period. The function rapidly changes - from down to up at points where the sine function equals one ( ).This is where any Spline interpolation has problems. We have 100 fitted nodes but at the points where the function should be equal to zero the interpolation has a quite different value. The only way to improve the Hermite interpolation is to increase the number of points and in our case we have increased them to 1000.

Graph 32. Function - Hermite Spline Interpolation (green curve) with 100 fitted nodes and Linear interpolation (blue curve) with 1000 fitted nodes. It is obvious that using 100 nodes does not produce a good result especially at the trough points.

Graph 33. Zoomed Graph32. Function - Hermite Spline Interpolation (green curve) with 100 nodes and Linear interpolation (blue curve) with 1000 nodes. We can see at the trough points Hermite Spline creates a smooth function but the actual function has sharp edges.