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
>
>
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> Abs[Zeta[1/2 + I*t]]/t^(1/4)
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> for t large, say, t< 10^10.
>
>
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> The trouble with NMaximize is that (sometimes) only local maxima are picked up.
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> When plotting, say
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> Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 3, 10^5}, PlotRange -> Full]
>
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> 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}.
>
>
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> Does anyone have any solutions other than plotting blocks of 10^k, 10^(k+1)?

```

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