Finding Maximum without a plot
- To: mathgroup at smc.vnet.net
- Subject: [mg129798] Finding Maximum without a plot
- From: Tim Trudgian <tim.trudgian at gmail.com>
- Date: Thu, 14 Feb 2013 02:11:19 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
- Delivered-to: mathgroup-newsend@smc.vnet.net
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)?