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MathGroup Archive 2004

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Re: Re: How to solve nonlinear equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52585] Re: Re: How to solve nonlinear equations?
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 3 Dec 2004 03:53:43 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <cohj9d$1nr$1@smc.vnet.net> <200412011057.FAA19914@smc.vnet.net> <comgo1$89e$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

the problem will never solved by  Mathematica
when the input uses a invalid syntax and the original posting
say nothing about the desired precision. But from the
equations it is easy to see that one nneds several hundred
digits.

Regards
  Jens

"DrBob" <drbob at bigfoot.com> schrieb im Newsbeitrag 
news:comgo1$89e$1 at smc.vnet.net...
> The only trouble with THAT is that it doesn't work.
>
> eqns = {20.428836553499018 - Log[X1] == 468/67*X1 + 5790/1273*X2 - 
> 66257/1273*
>         X3 - 24660/1273*X4 - 79150/1273*X5, 17.011108423692498 -
>            Log[X2] == 5790/1273*X1 + 6294/1273*X2 - 66257/1273*X3 - 24660/
>           1273*X4 - 403.8069285*
>             X5, -29.72639373695347 - Log[X3] == -66257/1273*
>           X1 - 66257/1273*X2 - 2*
>         X3, -26.273726271581616 - Log[X4] == -24660/1273*X1 - 24660/
>           1273*X2 + 10.15330715*X4, -38.76695085346396 - Log[X5] 
> == -79150/
>           1273*X1 - 403.8069285*X2 - 10.67374705*X5};
>
> FindRoot[eqns, {{X1, 1}, {X2, 1}, {X3, 1}, {X4, 1}, {X5, 1}}]
> eqns /. Equal -> Subtract /. %
>
> (FindRoot::lstol error)
> {X1 -> 0.5287215008048355 + 0.0078093799604902845*I,
>   X2 -> 0.002514442570050682 - 0.007506800892680369*I,
>   X3 -> 0.2750175495952261 + 0.0051666476248725625*I,
>   X4 -> -1.6157105189511614 -4.778719413301337*^-15*I,
>   X5 -> -0.006058532522555838 - 0.003759309847863656*I}
> {-0.0000172993518866571 - 5.25106242902848*^-7*I,
>   0.0014397436481736747 + 0.000060457451791506855*I,
>   -0.23588972784670026 + 0.007297504899863284*I,
>   -0.057825246363192695 + 3.1474540831359445*I,
>   0.0009303265262765592 + 0.00036856201666024546*I}
>
> Bobby
>
> On Wed, 1 Dec 2004 05:57:41 -0500 (EST), Jens-Peer Kuska 
> <kuska at informatik.uni-leipzig.de> wrote:
>
>> Hi,
>>
>> a) learn the correct syntax of Mathematica
>> b) read the Mathematica book carefully
>> c) type:
>>
>> eqns = {20.428836553499018 - Log[X1] ==
>> 468/67*X1 + 5790/1273*X2 - 66257/1273*X3 - 24660/1273*X4 -
>> 79150/1273*X5,
>> 17.011108423692498 - Log[X2] ==
>> 5790/1273*X1 + 6294/1273*X2 - 66257/1273*X3 - 24660/1273*X4 -
>> 403.8069285*X5, -29.72639373695347 - Log[X3] == -66257/1273*X1 -
>> 66257/1273*X2 - 2*X3, -26.273726271581616 -
>> Log[X4] == -24660/1273*X1 - 24660/1273*X2 +
>> 10.15330715*X4, -38.76695085346396 - Log[X5] == -79150/1273*X1 -
>> 403.8069285*X2 - 10.67374705*X5}
>>
>> FindRoot[eqns, {{X1, 1}, {X2, 1}, {X3, 1}, {X4, 1}, {X5, 1}}]
>>
>>
>>
>> Regards
>>
>>   Jens
>>
>>
>> "Wei Wang" <weiwang at baosteel.com> schrieb im Newsbeitrag
>> news:cohj9d$1nr$1 at smc.vnet.net...
>>> How to solve the following equations, where X1, X2, X3, X4 and X5 are
>>> variables?
>>>
>>> eqns = {20.428836553499018-ln(X1) ==
>>> 468/67*X1+5790/1273*X2-66257/1273*X3-24660/1273*X4-79150/1273*X5,
>>> 17.011108423692498-ln(X2) ==
>>> 5790/1273*X1+6294/1273*X2-66257/1273*X3-24660/1273*X4-403.8069285*X5, -29.72639373695347-ln(X3)
>>> == -66257/1273*X1-66257/1273*X2-2*X3, -26.273726271581616-ln(X4)
>>> == -24660/1273*X1-24660/1273*X2+10.15330715*X4, -38.76695085346396-ln(X5)
>>> == -79150/1273*X1-403.8069285*X2-10.67374705*X5};
>>>
>>
>>
>>
>>
>>
>
>
>
> -- 
> DrBob at bigfoot.com
> www.eclecticdreams.net
> 



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