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From: roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson)
Newsgroups: comp.soft-sys.matlab
Subject: Re: Solve Equation Symbolically
Date: Wed, 14 Nov 2007 07:52:20 +0000 (UTC)
Organization: National Research Council Canada - Conseil national de rechereches Canada
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In article <fhd1pu$j8d$1@fred.mathworks.com>,
evan klinger <eklinger1-nospam@cox.net> wrote:
>roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in
>message <fhb2v2$jqi$1@canopus.cc.umanitoba.ca>...

>> 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.

>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

cv12 has no real solutions if cv0 > db, which is a possibility
under the constraints you have given (db "in the millions"
could be as low as 1 million; cv0 up to "a few million"
could exceed that value.)

I tried each combination of the lower and upper value you gave
for each parameter. Taking only the extremes, there were
real roots for each case unless cv0 > db. The cases that had
only one real root, that root was >= 0. The cases that had
two real roots, the second root was < 0.

In random trials over the range of parameters, -usually- there was
one positive and one negative root, but in one of the cases there
were only two negative roots. In one of the cases, the positive root
was about +46 instead of the typical 0.08 - 0.25 range. That's going
to make it difficult to give good starting guesses for the ranges,
since your precision will usually be completely washed out before x = 4.
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