Re: Interesting Solution to a quartic eqn
- From: Peter <pwolynes@xxxxxxxxx>
- Date: Sat, 13 Feb 2010 21:42:38 -0800 (PST)
Hi Professor Magidin:
Sorry about the error in my last post. I am pretty sure that for the
counter-example you produced (which is essentially when either a = 0
and |b|=1 or b=0 and |a|=1), you'll still have solutions, but you'll
lose the uniqueness part. Uniqueness will only hold when both a_0 and
b_0 ne zero and none of the a_j and b_j for j=1,...,n-2 which are
generated by this process, are zero also.
I hadn't considered the equations associated with (c2) to be
constraints, but now that you pointed this out, it makes sense.
Thank-you once again for the insights: I don't think I would have seen
most of them!
This problem is a small part of a much larger problem that deals with
fitting atmospheric tidal velocities to a model. Nevertheless, I'd
like to acknowledge your contribution to helping us better understand
the math behind this solution, with your permission of course.