This is a problem of oscillation at the edges of an interval/size class and can produce error fits that can get larger, not smaller, with increasing number of terms.
Without using a cubic spline fit....
Runge's phenomenon is generated by using the same high-degree polynomial over the whole interval. Any local, piecewise polynomial (finite-element-like) approximation will do a much better job in nonsmooth cases. In fact, splines are defined in a somewhat global form, and might not even be the best choice in this respect.
Zoleikha Soori
Seems to be a screenshot of a paper title but not the paper itself...
An easy (though rather computationally expensive) alternative is to use a Bernstein polynomials approximation.
To avoid Runge's phenomena (i.e., oscillations) that occur when interpolating with polynomials of higher degrees, it is recommended to use lower degree polynomials, especially cubic splines).
Tekle Gemechu
Did you see the last sentence in my question? ['Without using a cubic spline fit....']
Get an attached file! Short note on interpolation.
Many thanks for sharing!
One may read the file I attached (last week). It contains different interpolation methods.
The choice of an interpolation model most generally depends on the nature of the data to be modeled. We have to try different interpolations for our data and compare their accuracy. Theorems on convergence & error analysis on each model type has to be studied, where needed.
Many thanks!
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