       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:=
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:=NSolve[eqs]

Out={}

But

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

Out:=
{{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.

```