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FindRoot Precision Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg73302] FindRoot Precision Problem
• From: Scott Kasen <sdk5n at virginia.edu>
• Date: Fri, 9 Feb 2007 23:45:25 -0500 (EST)

I'm running Mathematica 5.1 and have been struggling with this problem 
for the last few days...

I'm trying to use FindRoot to do a simultaneous solve on five equations 
involving five unknown variables.  Unfortunately for me, I continued 
getting the "Encountered a Singular Jacobian" error not far from my 
guess values.

In my attempts at debugging, I noticed the following peculiarity (I'm 
giving a very simplified example below):

If one of my equations is:
x1+x2 = = 0
then FindRoot is able to converge successfully.

However, if I change the equation to:
x1*100+x2*100 = = 0
I get the "Singular Jacobian" error.  It is this latter equation type 
that I need to be able to solve (i.e. the one with larger orders of 
magnitude.)

It is for this reason that I feel my problem is related to precision and 
accuracy.

I've tried playing around with the precision and accuracy, but to no 
avail.  A couple of things I've tried:  changing my PrecisionGoal, 
AccuracyGoal, and WorkingPrecision parameters, as well as globally 
increasing my precision using $MinPrecision.  My search of the math 
group archive pulled this up written by Daniel Lichtblau:
http://forums.wolfram.com/mathgroup/archive/1998/Mar/msg00336.html
This is hauntingly similar to my problem, and it is solved here using 
the GroebnerBasis function.  But, in my situation, my equations are 
nonlinear...I have some exponentials in my equations, and the 
GroebnerBasis function reminds me of that by producing the error, 
"Equations appear to be solved in an essentially non-algebraic way".

Any help would be immensely appreciated!  I've included the actual five 
equations in a Mathematica notebook file at the URL below, along with my 
FindRoot call and guesses.  I've tried to clean the equations up a 
little bit using Simplify before making this notebook file.

http://people.virginia.edu/~sdk5n/math_group.nb


-- 
______________________

Scott D. Kasen
Graduate Research Assistant

Department of Materials Science and Engineering
University of Virginia
P.O. Box 400745
116 Engineers Way
Charlottesville, VA 22904-4745

email:sdk5n at virginia.edu
voice: 434-982-5675
fax: 434-982-5660