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MathGroup Archive 2000

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Re: Can Mathematica 4 do this?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24528] Re: Can Mathematica 4 do this?
  • From: mend0070 at garnet.tc.umn.edu (Philip C Mendelsohn)
  • Date: Mon, 24 Jul 2000 03:04:08 -0400 (EDT)
  • Organization: University of Minnesota, Twin Cities Campus
  • References: <8l699m$sdi@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hyun Go (mathcunix at yahoo.com) wrote:
: Hi all,

: I'm trying to solve a system of 8 equations with 8
: unknowns using Solve --by simply making them into a
: system of simultaneous equation and let Solve run.
: However, the calculation's been running for more than
: 40 mins so far and I'm still waiting (I have set
: $RecursionLimit = 2000). 

: All 8 equations in the system are non-linear; Should I
: stop trying it with Mathematica, or is there any
: command more appropriate in dealing with non-linear
: equations?
: Thanks,

I don't think that Solve will do non-linear equations.  

If you can write your equations in the form A . x == b,
you can use a form of Newton's method to solve numerically
in an iterative fashion.

Subtracting b from both sides results in a vector valued function
that equals 0.  If you start with an initial x0, (A . x0) - b = epsilon,
where epsilon is some error (i.e., not 0.)

If you then solve -J deltaX = epsilon, where J is the jacobian of your
function for deltaX.  Then your next value of x1 == x0 + delta x .

If things work out well, your x should converge.

I have code for a similar problem, but am unable to include it in this
post.  Either e-mail me, or I will try and post it later today.

Hope that helps,

Phil Mendelsohn 


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