Re: Unstable Simultaneous Linear Equations!

On Thu, 3 Apr 2008 18:14:51 -0700 (PDT), monir <monirg@xxxxxxxxxxxx> wrote:

<SNIP>

3) On the other hand, the elliptic interpolation curve appears to
satisfy all the conditions and requirements. It's critical, however,
that one applies the correct scenario in constructing the applicable
curve segment of the ellipse. The 4 possible scenarios were described
earlier (my post April 1, 12:20 am local).
The applicable scenario for the provided example is scen2

4) As a footnote, Dave Dodson has insisted that in the elliptic
interpolation procedure a "cusp" exists where the ellipse joins the
(analytical) curve at point P2.
Dave's observation suggests that although the elliptic curve and the
analytical curve share the same coordinates (x2,y2) and have the same
slope (dy/dx) at P2, the elliptic curve nevertheless has a cusp at
that point!
I haven't personally observed or been able to locate such abnormality
at or near P2 in any of the 10s test cases.
Have you observed a cusp at P2 ??

Any comments ? Thank you.
Monir

I think what Dave is talking about is something that I also wondered about.

Your elliptic curve does have the right slope at P2, but if you follow the path
along the elliptic curve from P1 to P2, when you arrive at P2 you are going down
and to the left. Can you show some of the points in your analytical function
that are outside the interval P1 < x < P1? I assumed that as you approach P2
from the left, you would want to be moving up and to the right.

As Dave pointed out in another post, if that is the case, then if you want a
slope of 132.533+ at P2 you will have to be approaching from below and the
interpolating curve will have to have a minimum as the cubic does.

Your elliptic curls around as it approaches P2; surely that isn't what you want,
is it?

.

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