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