On 4/30/2012 2:17, someone wrote:
On 04/30/2012 12:39 AM, Kiuhnm wrote:
So Matlab at least warns about "Matrix is close to singular or badly
scaled", which python (and I guess most other languages) does not...
A is not just close to singular: it's singular!
Ok. When do you define it to be singular, btw?
Which is the most accurate/best, even for such a bad matrix? Is it
possible to say something about that? Looks like python has a lot more
digits but maybe that's just a random result... I mean.... Element 1,1 =
2.81e14 in Python, but something like 3e14 in Matlab and so forth -
there's a small difference in the results...
Both results are *wrong*: no inverse exists.
What's the best solution of the two wrong ones? Best least-squares
solution or whatever?
Trust me. They're both so wrong that it doesn't matter.
Have a look at A*inv(A) and inv(A)*A and you'll see by yourself.
With python, I would also kindly ask about how to avoid this problem in
the future, I mean, this maybe means that I have to check the condition
number at all times before doing anything at all ? How to do that?
If cond(A) is high, you're trying to solve your problem the wrong way.
So you're saying that in another language (python) I should check the
condition number, before solving anything?
Yes, unless you already know that it will always be low by design.
You should try to avoid matrix inversion altogether if that's the case.
For instance you shouldn't invert a matrix just to solve a linear system.
What then?
Look at the documentation of the library you're using.
Cramer's rule?
Surprisingly, yes. That's an option. See
"A condensation-based application of Cramerʼs rule for solving
large-scale linear systems"
Popular linear codes are based on Gaussian elimination or some iterative
method, though.
Kiuhnm
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