Re: FindRoot anomaly (example from Mathematica Tutorial)

• To: mathgroup at smc.vnet.net
• Subject: [mg72201] Re: [mg72118] FindRoot anomaly (example from Mathematica Tutorial)
• From: gardyloo <gardyloo at mail.wsu.edu>
• Date: Thu, 14 Dec 2006 05:49:25 -0500 (EST)
• References: <200612131138.GAA23570@smc.vnet.net>

```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
gardyloo at mail.remove_this.wsu.and_this.edu
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```

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