Re: How can I use FindMaximum to get a result better than MachinePrecision?
- To: mathgroup at smc.vnet.net
- Subject: [mg127963] Re: How can I use FindMaximum to get a result better than MachinePrecision?
- From: Bill Rowe <readnews at sbcglobal.net>
- Date: Wed, 5 Sep 2012 03:10:50 -0400 (EDT)
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- Delivered-to: l-mathgroup@wolfram.com
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On 9/4/12 at 5:45 AM, drkirkby at gmail.com (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]
>Any suggestions?
Try:
FindMaximum[8 E^(-x) Sin[x] -1,{x,0,8},WorkingPrecision->25]
or whatever you desire. Also note:
In[14]:= D[8 E^(-x) Sin[x] - 1, x]
Out[14]= (8*Cos[x])/E^x - (8*Sin[x])/E^x
Which clearly indicates a minima or maxima occurs when Sin[x] ==
Cos[x]. Given the result is multiplied by Exp[-x], it is clear
you want x to be as small of a positive number as possible to
get a maximum. So, the maximum must occur at Pi/4 exactly