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