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Re: Partial derviatives in mathematica

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

In article <glmsqr$mik$1 at>, xareon at wrote:


> 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}


> 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,

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


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