Re: Plot vs NMaximize
- To: mathgroup at smc.vnet.net
- Subject: [mg94262] Re: [mg94221] Plot vs NMaximize
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Tue, 9 Dec 2008 06:59:15 -0500 (EST)
- References: <200812081122.GAA15842@smc.vnet.net>
- Reply-to: drmajorbob at longhorns.com
I sent a RootSearch link, where the following would be more appropriate: http://library.wolfram.com/infocenter/MathSource/6725/ Other searches at MathSource might get you closer to what you want. Bobby On Mon, 08 Dec 2008 08:56:48 -0600, Nikolaus Rath <Nikolaus at rath.org> wrote: > DrMajorBob <btreat1 at austin.rr.com> writes: >> Here's an example of using Plot to help FindMaximum: >> >> pts =.; >> f = Sin[2 x] Cos[3 x]; >> p1 = Plot[f, {x, 0, 2 Pi}]; >> xpts = First@Cases[p1, Line[pts : _] :> pts, Infinity]; >> p2 = ListPlot[xpts]; >> Show[p1, p2] >> >> (graphic omitted) >> >> max = SortBy[xpts, Last][[-1, 1]] >> FindMaximum[f, {x, max}] >> >> 5.31784 >> >> {0.907858, {x -> 5.31789}} >> >> Plot got very close to the max in that interval, and FindMaximum uses >> the result as an advanced start. > > Interesting. I thought about the same thing, but I didn't expect that > it can be coded so easily. > >> FindMaximum doesn't do it this way automatically, because it >> wouldn't always be best. You can never be certain, in fact, that >> Plot finds the global maximum. > > Yes. But the same is true for NMaximize, so I do not understand why > the two functions use different methods when they (as I see it) give > the same result, only once as a graphic and once as a number. > > Do you have an example where it would not be sensible to have > NMaximize find the same maximum that Plot shows? > > > > Best, > > -Nikolaus > -- DrMajorBob at longhorns.com
- References:
- Plot vs NMaximize
- From: Nikolaus Rath <Nikolaus@rath.org>
- Plot vs NMaximize