Efficient repeated use of FindRoot

*To*: mathgroup at smc.vnet.net*Subject*: [mg74049] Efficient repeated use of FindRoot*From*: "Michael A. Gilchrist" <mikeg at utk.edu>*Date*: Wed, 7 Mar 2007 03:16:53 -0500 (EST)

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 -----------------------------------------------------

**Follow-Ups**:**Re: Efficient repeated use of FindRoot***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: Efficient repeated use of FindRoot***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: Efficient repeated use of FindRoot***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: Efficient repeated use of FindRoot***From:*"Michael A. Gilchrist" <mikeg@utk.edu>

**Re: Efficient repeated use of FindRoot***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: Efficient repeated use of FindRoot***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: Efficient repeated use of FindRoot***From:*"Chris Chiasson" <chris@chiasson.name>