- #1
bruno67
- 32
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I have to interpolate a function between a small number of points n (say, 3-5), at which I know both the value of the function and its first derivative. Normally, this would be a good candidate for polynomial interpolation.
The only problem is that at the first point the function is only once differentiable (its second derivative is infinite), while it is perfectly smooth in the rest of the interval. How can I get an estimate of the interpolation error? The usual estimate found in textbooks requires the function to have at least n+1 continuous derivatives in the closed interval in which one is interpolating.
Thanks.
The only problem is that at the first point the function is only once differentiable (its second derivative is infinite), while it is perfectly smooth in the rest of the interval. How can I get an estimate of the interpolation error? The usual estimate found in textbooks requires the function to have at least n+1 continuous derivatives in the closed interval in which one is interpolating.
Thanks.