Re: Partial derviatives in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg95815] Re: Partial derviatives in mathematica
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 28 Jan 2009 06:28:27 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <glk1na\$los\$1@smc.vnet.net> <glk80p\$o86\$1@smc.vnet.net> <glmsqr\$mik\$1@smc.vnet.net>

```In article <glmsqr\$mik\$1 at smc.vnet.net>, xareon at gmail.com wrote:

[snip]

> thank you for your support, with your hints i've finally managed it to
> work. What does it mean that i get this output?
>
> In[46]:= NewtonSystem[{60, 0.0001251648904560967}, 30];
> F[{60, 0.000125165}]={-0.0798194, -32172.1}
>
> Inverse::luc: Result for Inverse of badly conditioned matrix
>                                                    8
>     {{-0.0138889, -2725.54}, {-2725.54, -9.88747 10 }} may contain
> significant numerical errors.
> F[{61.3904, 0.0000887939}]={0.0295066, 20324.7}

[snip]

> I can't understand the error i'm getting: Inverse::luc: Result for
> Inverse of badly conditioned matrix
>
> It seems like a warning, is it relevant?

Highly relevant, because it is all about the confidence you can have in
the numerical result retuned. From "tutorial/MatrixInversion":

"When you invert an approximate numerical matrix, Mathematica can
usually not tell for certain whether or not the matrix is singular: all
it can tell is, for example, that the determinant is small compared to
the entries of the matrix. When Mathematica suspects that you are trying
to invert a singular numerical matrix, it prints a warning."

So Mathematica prints a warning and it is up to you to decide whether
the result is valid or not.

If you are not familiar with condition numbers,

http://planetmath.org/encyclopedia/MatrixConditionNumber.html

http://en.wikipedia.org/wiki/Condition_number

might be good starting points. (Do not forget to check the references
given by these two web sites.)

Regards,
--Jean-Marc

```

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