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From: "evan klinger" <eklinger1-nospam@cox.net>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Solve Equation Symbolically
Date: Tue, 13 Nov 2007 20:35:10 +0000 (UTC)
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roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in
message <fhb2v2$jqi$1@canopus.cc.umanitoba.ca>...
> In article <fhajsd$bcg$1@fred.mathworks.com>,
> evan klinger <eklinger1-nospam@cox.net> wrote:
> >roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in
> >message <fhaiam$k8$1@canopus.cc.umanitoba.ca>...
> >> In article <fhag57$bca$1@fred.mathworks.com>,
> >> evan klinger <eklinger1-nospam@cox.net> wrote:
> >> >Is there a way to increase the 25,000 character limit? I
> >> >really need to solve up to cv12,
> 
> >> you are trying to find the closed form solution to a
> >polynomial
> >> of order 12 that does not happen to be factorable down
> 
> >So what are my options here? I would like a closed form
> >solution so that I can plug in values into the variables
> >directly and solve, but if that's not possible, is there any
> >alternative?
> 
> What kind of ranges of values can your constants take?
> I've been playing around with some test values, and it
looks to
> me as if you could easily encounter severe problems with
loss of
> precision in your calculations, especially if cr > 2.
> 
> With random values between -1 and 1 for the cv12 variables, it
> was fairly common in my trials for there to be an x root
somewhere
> just a bit more than 2, but that by x = 3 that the
function value
> had risen beyond 10^8 or 10^9 -- but with another one of
my trials,
> the roots ranged from -7 to +4 . 
> 
> Unless your values (especially cr) are fairly small, I suspect
> you will lose precision so quickly as to make it very
doubtful that
> you would be able to accurately find the equation roots.
> 
> cr is the biggest contribution to the problem: as well as
> cv12 being a 12th order polynomial in x, it is also a 12th
order
> polynomial in cr (cr and x will have the same polynomial order
> as each other in each cv*). Thus even a small change in cr can
> make a big change in the x roots. And a small change in cr can
> result in -different- 12th order roots becoming the
real-valued
> roots, so even if you had an closed form solution for one
of the
> 12th-order roots, that root might become imaginary with a
small
> change in parameters.
> 
> For example, in a particular trial I did
> with random values for the parameters except p3, for p3=1/3,
> the first and 7th roots were the real roots, but for p3=1/2,
> the 6th and 7th roots were the real roots -- and p3
appears only
> in its first power in cv12.
> 
> 
> If I recall correctly, I have seen mention of a FEX
contribution
> that generalizes fzero() to find multiple roots. You are
> probably going to have to use something like that, and to
> figure out what you want to do with the multiple roots
that are
> found, but with some kinds of checks in place to ensure
that you
> are not finding spurious roots (or failing to find valid
roots)
> due to loss of precision.
> -- 
> We regret to announce that sub-millibarn resolution
bio-hyperdimensional
> plasmatic space polyimaging has been delayed until the release
> of Windows Vista SP2.

cr will always be between 0 and 1
db will be in the millions
p is usually between 0 and 1,000,000
cv[n] is usually between 0 and a few million

This is related to cost of insurance for a life insurance policy