On Sep 29, 1:54 pm, hagman <goo...@von-eitzen.de> wrote:
> 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)

Also, interpolating a polynomial at 10 random
points is not apt to give a good approximation
on an interval.  In most cases the polynomial
chosen in this way will oscillate wildly in
between the interpolation points.

--c