Re: using FindRoot to find multiple answers in a domain?

• To: mathgroup at smc.vnet.net
• Subject: [mg69261] Re: using FindRoot to find multiple answers in a domain?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 4 Sep 2006 02:41:25 -0400 (EDT)
• Organization: The University of Western Australia
• References: <ed0rn9\$sm6\$1@smc.vnet.net> <ed3rou\$rv5\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <ed3rou\$rv5\$1 at smc.vnet.net>, "akil" <akomur at wanadoo.nl>
wrote:

> IntervalRoots package and RootSearch do not work for the kind of formulas I
> have.

Are you sure?

> For example in the domain [0,Pi/2] we want to solve (I only used FindRoot
> because this was the fastest):
>
> I put the package I test in on
> http://home.wanadoo.nl/akomur/testRootSearch.nb so that you can see the
> formulas I use.
>
> Copying them In here ruins the formulas.

Copy as Plain text. Your first formula is

nlv = Max[-81.24275115593154  Cot[beta] - 48.489352280270914,
Min[-46.844746272761526 Cot[beta] - 71.4213555357176,
-46.480384751324436 Cot[beta] - 71.66426321667566]]

Note that PiecewiseExpand can be applied to such formulae. If you
simplify the result

Simplify[PiecewiseExpand[nlv]]

you deduce that nlv is just

-81.24275115593154  Cot[beta] - 48.489352280270914 if Cot[beta] <= 2/3

-46.844746272761526 Cot[beta] - 71.4213555357176 if Cot[beta] >= 2/3

You can check that these values are consistent when Cot[beta] == 2/3.
Moreover, the catch-all condition

-46.480384751324436 Cot[beta] - 71.66426321667566

is redundant for real beta since it only applies when Cot[beta] == 2/3.
A brief examination of nuvb shows that it involves ratios of (powers of)
expressions similar to nlv. I expect that simplification of these
expressions prior to constructing nuvb would lead to a final form that
is not that hard to handle.

I expect that if you step back and tell us more about the original
problem, then a more elegant approach would present itself.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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