Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2009

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

Search the Archive

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


  • Prev by Date: domains as sets
  • Next by Date: Re: Re: Non-deterministic numerical inaccuracies in
  • Previous by thread: Re: Partial derviatives in mathematica
  • Next by thread: Re: Destructuring arguments to pure functions?