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Re: FindRoot anomaly (example from Mathematica Tutorial)


And yet the solutions you get from that FindRoot are mostly incorrect.
Apparently, the default method that FindRoot is using gets hung up when
Cos[x] is approximately +/- 1 (after all, the Newton's method is
expected to go wonky at these particular points). So, for example, the
"root" x->56.542772508541205` (just to pick one at random) does NOT
satisfy the original equation.
   Ersek's RootSearch function finds only seven roots to the equation
between x = 1 and x = 100:

sol = RootSearch[3*Cos[x] == Log[x], {x, 1, 100}]

{{x -> 1.447258617277903}, {x -> 5.301987341712279},
  {x -> 7.13951454299577}, {x -> 11.970165552607465},
  {x -> 13.10638768062491}, {x -> 18.624716143898215},
  {x -> 19.0387370100137}}

Possibly ( I haven't tried it) forcing FindRoot to use the secant method
by supplying different starting conditions might make for a more
stringent search.

         Regards,
                  C.O.

howardfink at gmail.com wrote:
> FindRoot[3Cos[x] == Log[x], {x, 1}] is on page 12 of the tutorial that
> starts up in Mathematica 5.
> I was interested in how the seed affects the answer, so I made a table
>
> sol = Table[FindRoot[3Cos[x] == Log[x], {x, b}], {b, 100}];
>
> and then plotted the solutions
>
> ListPlot[x /. sol]
>
> I got a nice table, but the seed of 22 returns  {x -> -207.932 +
> 1.39227 i]}
>
> so the plot returns the error:
> Graphics::gptn: Coordinate -207.932 + 1.39227\\[ImaginaryI] in {22,
> -207.932 \
> + 1.39227\\[ImaginaryI]} is not a floating-point number.
>
> The other 99 results make a nice plot.
>
>
>   

-- 
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Curtis Osterhoudt          
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