Re: How can I use FindMaximum to get a result better than MachinePrecision?

• To: mathgroup at smc.vnet.net
• Subject: [mg127952] Re: How can I use FindMaximum to get a result better than MachinePrecision?
• From: "danl at wolfram.com" <daniel.lichtblau0 at gmail.com>
• Date: Wed, 5 Sep 2012 03:07:09 -0400 (EDT)
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• References: <k24irq\$1k9\$1@smc.vnet.net>

```On Tuesday, September 4, 2012 4:50:53 AM UTC-5, David Kirkby wrote:
> I've tried this:
>
> In[2]:= FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8}]
>
> Out[2]= {1.57918, {x -> 0.785398}}
>
> Then played around to try to get a more accurate result.
>
> In[9]:= FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},AccuracyGoal->20, PrecisionGoal->20]
>
> Out[9]= {1.57918, {x -> 0.785398}}
>
> In[10]:= Precision[%]
>
> Also:
>
> In[7]:= N[FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},AccuracyGoal->200, PrecisionGoal->200],100]
>
> Out[7]= {1.57918, {x -> 0.785398}}
>
> In[8]:= Precision[%]
>
> Out[8]= MachinePrecision
>
> Any suggestions?

Raise WorkingPrecision.

FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},AccuracyGoal->20, PrecisionGoal->20, WorkingPrecision->30]

Out[2]= {1.57917553555867559401893547648,

>    {x -> 0.785398163397448309705386001198}}

See Help > Documentation Center > PrecisionGoal > More Information > 5th bullet item.

related: Help > Documentation Center > FindMaximum > Options > AccuracyGoal & PrecisionGoal 2nd and 3rd examples.

Daniel Lichtblau
Wolfram Research

```

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