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

• To: mathgroup at smc.vnet.net
• Subject: [mg127961] Re: How can I use FindMaximum to get a result better than MachinePrecision?
• From: Ray Koopman <koopman at sfu.ca>
• Date: Wed, 5 Sep 2012 03:10:10 -0400 (EDT)
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• References: <k24irq\$1k9\$1@smc.vnet.net>

```On Sep 4, 2:50 am, David Kirkby <drkir... at gmail.com> 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?

FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},
AccuracyGoal->30, PrecisionGoal->30, WorkingPrecision->40]

{1.579175535558675594018935476481035678702,
{x -> 0.7853981633974483096234856042864548995134}}

```

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