merit_2
Posts:
3
Registered:
4/28/12


Re: Finding Maximum without a plot
Posted:
Feb 15, 2013 1:56 AM


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 UTC7, 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)?

