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Re: Re: Re: How to solve nonlinear equations?

• To: mathgroup at smc.vnet.net
• Subject: [mg52617] Re: [mg52585] Re: Re: How to solve nonlinear equations?
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 4 Dec 2004 04:07:56 -0500 (EST)
• References: <cohj9d$1nr$1@smc.vnet.net> <200412011057.FAA19914@smc.vnet.net> <comgo1$89e$1@smc.vnet.net> <200412030853.DAA26057@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

Neither of us has answered the original question, which was "How to solve...".

Let's say we need 200 digits. How do you solve it?

Bobby

On Fri, 3 Dec 2004 03:53:43 -0500 (EST), Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote:

> 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
>>
>
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net

• Follow-Ups:
  • Re: Re: Re: Re: How to solve nonlinear equations?
    • From: Daniel Lichtblau <danl@wolfram.com>

• References:
  • Re: How to solve nonlinear equations?
    • From: "Jens-Peer Kuska" <kuska@informatik.uni-leipzig.de>
  • Re: Re: How to solve nonlinear equations?
    • From: "Jens-Peer Kuska" <kuska@informatik.uni-leipzig.de>