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MathGroup Archive 2006

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Re: Points sampled by FindMinimum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71221] Re: Points sampled by FindMinimum
  • From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
  • Date: Fri, 10 Nov 2006 06:38:56 -0500 (EST)
  • References: <eisfsu$mrp$1@smc.vnet.net><eiut0d$h42$1@smc.vnet.net>

Thanks for your responses. I see now that Mathematica is evaluating the
function at three nearby points as part of its finite-difference
approximation to the derivative.

Cheers,
Andrew


On Nov 9, 8:39 pm, "dimitris" <dimmec... at yahoo.com> wrote:
> See the following commands
>
> FindMinimum[func[x], {x, 0.1}, EvaluationMonitor :> Print[x]]
> 0.1
> 0.1
> 0.10000000149011612
> 0.6
> 0.6
> 0.6000000089406967
> 0.9999999776482598
> 0.9999999776482598
> 0.9999999925494206
> 0.9999999925494208
> 0.9999999925494208
> 1.000000007450582
>
> {1., {{a, {2, 28}} -> 0.9999999925494208}}
>
> FindMinimum[func[x], {x, 0.1}, StepMonitor :> Print[x]]
> 0.6
> 0.9999999776482598
> 0.9999999925494208
> {1., {{a, {2, 28}} -> 0.9999999925494208}}
>
> After read carefully the reply of Andrzej Kozlowski to a similar query
> of mine
> regarding FindRoot which appeared here
>
> http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_...
>
> More specifiacally watch there he said that
>
> "... In general EvaluationMonitor (and also Print statement I add) will
> produce more
> values than StepMonitor, because it records each time the specified
> numerical
> function is evaluated. Sometimes to make one step in an iterative
> procedure you need to evaluate the function several times at
> different points (the standard example is when you need to compute a
> numerical derivative using finite differences) and all these
> computations will be part of one step (so will not be recorded by
> StepMonitor) but will be recored by EvaluationMonitor..."
> 
> Regards
> Dimitris


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