I have an ordered set of $n$ points $(x_1,y_1),\dots,(x_n,y_n)$ and I would like to choose an ordered subset of these points, say $(x_{k_1},y_{k_1}),\dots,(x_{k_s},y_{k_s})$, with $(x_{k_1},y_{k_1})=(x_1,y_1)$ and $(x_{k_s},y_{k_s})=(x_n,y_n)$ and such that they "best" fit the whole path.
How can I perform this?
You could make up a table of the divided differences up to the second degree, and discard the points that have a "low" 2nd div.difference with the points nearby.
The segments connecting the points remaining will pass "quite near" to the discarded ones.