Hermite Spline Interpolation

Function: - Hermite Spline Interpolation 2

This function when close to zero, has high density oscillations, which increase approaching zero, while the function ln(x) at exactly zero will be infinity. Therefore the function sin(ln(x)) will have a high speed changes (first derivative) value from -1 to 1 for ( ), and in that case , the number is going to zero if K is growing. If we use too small a node number it will result in the interpolation missing some of the maximums and minimums.

Graph 34. Function - Hermite Spline Interpolation (red curve). This Hermite Spline interpolation the peaks will be magnified to verify the Hermite curve in the next Graph 35.

Graph 35. Zoomed Graph 34. Function - Hermite Spline Interpolation (red curve). Compared to Akima Spline Hermit this is much better as the first three maximums are higher than the Akima Spline but is slightly less than the real function.