Re: FindRoot s all

• To: mathgroup at smc.vnet.net
• Subject: [mg49416] Re: [mg49415] FindRoot s all
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 19 Jul 2004 07:46:06 -0400 (EDT)
• References: <200407181209.IAA25955@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 18 Jul 2004, at 21:09, Narasimham G.L. wrote:

> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> y[u_,c_]=c^u-u^c-1 ;
> Plot[y[x,2],{x,-5,5}]; FindRoot[y[x,2]==0,{x,-5,5}];
> " Solution settles to a value outside the interval
> of roots of its derivative (humps and valleys),it may be
> the problem of Newton-Raphson diverging tangets.How to
> capture all roots [in this case {x -> 0, 1}] ? It should be
> valid for all c."
> TIA
>
>
I am not sure what you  mean by

> How to
> capture all roots [in this case {x -> 0, 1}] ?

the graph clearly shows three roots. FindRoot gives you one of them.
You can get them all (as discussed in this list recently) with

<<NumericalMath`IntervalRoots`

Mean/@(List@@(IntervalBisection[y[x,2],x,Interval[{-5.,5.}],.01,
MaxRecursion->10]))

{0.,1.00098,4.25781}

or using Ted Ersek's RootSearch package on MathSource.

Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

```

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