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Re: Finding Maximum without a plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129804] Re: Finding Maximum without a plot
  • From: richardgreco at gmail.com
  • Date: Fri, 15 Feb 2013 01:57:48 -0500 (EST)
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New in Mathematica 9 is MaxDetect[].
As an example:

rr = Abs[Zeta[1/2 + I*t]]/t^(1/4)

Abs[Zeta[1/2 + I t]]/t^(1/4)

kk = Table[rr, {t, 1, 1000}] // N;

In[5866]:= MaxDetect[kk, .5]

Out[5866]= {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, \
0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, \
0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, \
0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, \
0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1}


On Thursday, February 14, 2013 12:09:33 AM UTC-7, Tim Trudgian wrote:
> I should like to find the maximum of 
> 
> 
> 
> Abs[Zeta[1/2 + I*t]]/t^(1/4)
> 
> 
> 
> for t large, say, t< 10^10.
> 
> 
> 
> The trouble with NMaximize is that (sometimes) only local maxima are picked up. 
> 
> 
> 
> When plotting, say
> 
> 
> 
> Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 3, 10^5}, PlotRange -> Full]
> 
> 
> 
> I can see that, around t = 20,000, there is a value above 1.5. This value is not picked up when plotting the same function in the range {t, 3, 10^6}.
> 
> 
> 
> Does anyone have any solutions other than plotting blocks of 10^k, 10^(k+1)?




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