Re: Efficient repeated use of FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg74060] Re: [mg74049] Efficient repeated use of FindRoot
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Thu, 8 Mar 2007 04:35:00 -0500 (EST)
• References: <200703070816.DAA26723@smc.vnet.net>

```Why are you not using NMinimize or NMaximize?

On 3/7/07, Michael A. Gilchrist <mikeg at utk.edu> wrote:
> Hi all,
>
> I've got an optimization problem that I am trying to evaluate numerically
> and at a number of different points of a particular variable.  I am using
> a Lagrangian multiplier to impose a constraint on the optimization of the
> 'free variables' and as a result trying to find the root for a set of n
> coupled equations (in its full form n = 4000+ variables).
>
>
> Using some approximations I can come up with some reasonable initial
> conditions, but, as you might imagine, it takes quite some time to run
> the code.  Looking at the output it appears that the greatest amount of
> time is initialization of the FindRoot routine (once the routine is
> running it calculates each step quite quickly).
>
>
> Here's some pseudo code to illustrate the basic idea:
>
> (*set up eqns and variables*)
> Clear[m];
> vars = Table[m[i], {1, n}]
>
> eqns = Table[
>         (llik[i, vars] + \[Lambda] m[i] ==0), {i, 2, n}]
>                                 (*llik previously defined)
> ics =   Table[
>          m0[i] = T[i]/phi[i] (*T[i] and Phi[i] previously defined*),
>         {i, 2, n}];
>
> frvars = Table[{m[i], m0[i] * 0.01, m0[i]*10}, {i, 2, n}];
>
>
> (*look for solution to problem for multiple values of m[1] *)
> Table[
>         FindRoot[eqns, frvars], {m[1], 0.01, 0.2, 0.01}]
>
>
> I am aware of the NDSolve package StateData that allows one to
> efficiently evaluate DE's with various different initial
> conditions by processing the equations.
>
> I've looked through the documentation on FindRoot and haven't found a
> similar routine/ability.  I'm wondering if anyone has any ideas on how
> one might increase the efficiency of my calculations.
>
> Thanks.
>
> Mike
>
>
> -----------------------------------------------------
> Department of Ecology & Evolutionary Biology
> 569 Dabney Hall
> University of Tennessee
> Knoxville, TN 37996-1610
>
> phone:(865) 974-6453
> fax:  (865) 974-6042
>
> web: http://eeb.bio.utk.edu/gilchrist.asp
> -----------------------------------------------------
>
>
>

--
http://chris.chiasson.name/

```

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