       Re: 3 transcendent equations, 2 unknown variables

• To: mathgroup at smc.vnet.net
• Subject: [mg65887] Re: 3 transcendent equations, 2 unknown variables
• From: dh <dh at metrohm.ch>
• Date: Fri, 21 Apr 2006 01:33:20 -0400 (EDT)
• References: <e27jtm\$5de\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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.

Daniel

Ronaldo wrote:
> HI there,
>
> I have 3 independent equations (whose coefficients come from
> EXPERIMENTAL data).
> 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.
>

```

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