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