MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: 3 transcendent equations, 2 unknown variables

  • To: mathgroup at
  • Subject: [mg65887] Re: 3 transcendent equations, 2 unknown variables
  • From: dh <dh at>
  • Date: Fri, 21 Apr 2006 01:33:20 -0400 (EDT)
  • References: <e27jtm$5de$>
  • Sender: owner-wri-mathgroup at

Hi Ronaldo,
if you have more equations than variables then, in general, there is no 
exact solution. Therefore, you have to decide what you want. Often 
people are happy with a least square solution that minimizes the sum of 
squares of the errors (called residuals), called the L2 norm. You may 
also minimize the maximal deviation, called the L-Infinity Norm. There 
are many other posibilities, but least square is probably what you want.

In this case, you need to feed to FindRoot an expression that calculates 
   the sum of squared resuduals.


Ronaldo wrote:
> HI there,
> I have 3 independent equations (whose coefficients come from
> The equations are quite complicated and include trigonometric
> functions.
> There are 3 unknown variables.  So far, it looks fine, right ?
> However, there might be multiple solutions (due to the trigonometric
> functions). And I have no idea what initial values to enter in
> FindRoot, in order to get the real solutions.
> Suppose I find a separate method to determine one of the unknown
> variables.
> Then it will be nice to be able to use some approximation algorithm to
> find the other two variables by using not any two, but the three
> equations together.
> The problem is that FindRoot do not accept a number of equations
> different from the number of variables.
> This could be done in another system, but at the moment I am restricted to
> Mathematica only (and as you can guess from  my question I am a Newbie
> in Matemathica yet).
> Thank you for any advice !
> R.

  • Prev by Date: Re: command line question
  • Next by Date: Re: Where do I put my own add-on packages?
  • Previous by thread: 3 transcendent equations, 2 unknown variables
  • Next by thread: Re: problems with sum functions/ factoring the factorial-> I got it to work!