Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Re: Local extrema of a function of two variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90035] Re: [mg90017] Re: Local extrema of a function of two variables
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 27 Jun 2008 06:14:19 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200806260844.EAA21022@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

That's nice: I didn't know about the "trick" of getting the entire 
Hessian matrix in one simple expression D[f[x, y], {{x, y}, 2}], 
although of course it's documented at tutorial/Differentiation.

It's interesting that Mathematica (at least version 6) includes a System 
symbol Hessian...

   ?Hessian
System`Hessian
Attributes[Hessian] = {Protected}

...but apparently no associated definition and no reference page in the 
Documentation Center.

Jean-Marc Gulliet wrote:
>
> ...Now,we compute the Hessian matrix, *)
> 
> hessian = D[f[x, y], {{x, y}, 2}]
> 
> {{-12 x^2, 4}, {4, -12 y^2}}
> 
> (* and take its determinant: *)
> 
> d = hessian // Det
> 
> -16 + 144 x^2 y^2
 > ...
-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


  • Prev by Date: Re: Problem with NMaximize
  • Next by Date: Re: Re: font size too small
  • Previous by thread: Re: Local extrema of a function of two variables
  • Next by thread: standard error output