On 26 Sep., 21:38, "Jon" <jon8...@peoplepc.com> wrote:
> http://mypeoplepc.com/members/jon8338/math/id49.html
>
> This is the intersection of a line with a step graph.
>
> For 10^100 points, to save labor select 10 of them and find the curve that
> passes through them.  Solve the matrix for the coefficients of ten 9th
> degree polyomials.  Input the 10 abcissas into the independent variable of
> the equations to equal the 10 ordinates and solve for the coefficients using
> linear algebra.
>
> I'm sure this is common practice.  While the equation doesn't have to be a
> polynomial, all functions are power series anyway.  If the character is
> mostly manifested in the first 9 terms of the series, it works better.
>
> Jon Giffen

Not all functions are power series, not even all smooth functions
Also, a good approximation by a polynomal (in an interval) is a
totally different
taregt than approximating by a power series (around a point)