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problem with precision in NSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg15262] problem with precision in NSolve
• From: Enrique Zeleny Vazquez <ezelenyv at sirio.ifuap.buap.mx>
• Date: Wed, 30 Dec 1998 01:50:24 -0500
• Sender: owner-wri-mathgroup at wolfram.com

Hello Dear Mathgroupers:

I want to solve the following system of equations:

In[1]:= 
eqs=Flatten[{{389.6922999999999 == 
      358.7899539999999 - 28.742618*\[Eta]00 - 
       (0.25*(30.90234999999999 + 28.742618*\[Eta]00 + 
            10.54461599999999*\[Eta]02))/
        (-0.25 + 0.25*\[Eta]11) + 
       (0.25*(30.90234999999999 + 28.742618*\[Eta]00 + 
            10.54461599999999*\[Eta]02)*\[Eta]11)/
        (-0.25 + 0.25*\[Eta]11) - 
       330.0473359999999*\[Eta]20}, 
    {1236.820135999999 == 
      1184.533362 - 87.11028699999999*\[Eta]00 - 
       (0.25*(52.28677300000001 + 
            87.11028699999999*\[Eta]00 + 
            17.54739599999999*\[Eta]02))/
        (-0.25 + 0.25*\[Eta]11) + 
       (0.25*(52.28677300000001 + 
            87.11028699999999*\[Eta]00 + 
            17.54739599999999*\[Eta]02)*\[Eta]11)/
        (-0.25 + 0.25*\[Eta]11) - 
       97.42307499999999*\[Eta]20}, 
    {156.9444559999999 == 
      104.657683 - 87.11028699999999*\[Eta]00 - 
       (0.25*(52.28677399999992 + 
            87.11028699999999*\[Eta]00 + 
            97.42307499999999*\[Eta]02))/
        (-0.25 + 0.25*\[Eta]11) + 
       (0.25*(52.28677399999992 + 
            87.11028699999999*\[Eta]00 + 
            97.42307499999999*\[Eta]02)*\[Eta]11)/
        (-0.25 + 0.25*\[Eta]11) - 
       17.54739599999999*\[Eta]20}, 
    {70.18958399999999 == 
      39.28723399999999 - 28.742618*\[Eta]00 - 
       (0.25*(30.90234600000002 + 28.742618*\[Eta]00 + 
            330.0473359999999*\[Eta]02))/
        (-0.25 + 0.25*\[Eta]11) + 
       (0.25*(30.90234600000002 + 28.742618*\[Eta]00 + 
            330.0473359999999*\[Eta]02)*\[Eta]11)/
        (-0.25 + 0.25*\[Eta]11) - 10.54461599999999*\[Eta]20 }}];

In[2]:=NSolve[eqs]

Out[1]={}

But

In[3]:= 
(List@@#&/@
eqs/.{\[Eta]00 -> 0, \[Eta]20 -> 0, \[Eta]02 -> 0, 
   \[Eta]11 -> 0.5}

Out[3]:=
{{389.6922999999998, 389.6923039999998}, 
  {1236.820135999998, 1236.820134999999}, 
  {156.9444559999998, 156.9444569999999}, 
  {70.18958399999999, 70.18958}}

As you can see, this result is "almost" true, how can I force NSolve to
obtain this? I have tried NSolve[eqs,WorkingPrecision->8] with the same
result. I only need a result with say 5% of tolerance.

Thanks.