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