On 05/02/2012 01:52 PM, Steven D'Aprano wrote:
On Wed, 02 May 2012 08:00:44 +0200, someone wrote:
On 05/02/2012 01:05 AM, Paul Rubin wrote:
someone<newsbo...@gmail.com> writes:
Actually I know some... I just didn't think so much about, before
writing the question this as I should, I know theres also something
like singular value decomposition that I think can help solve
otherwise illposed problems,
You will probably get better advice if you are able to describe what
problem (ill-posed or otherwise) you are actually trying to solve. SVD
I don't understand what else I should write. I gave the singular matrix
and that's it.
You can't judge what an acceptable condition number is unless you know
what your data is.
http://mathworld.wolfram.com/ConditionNumber.html
http://en.wikipedia.org/wiki/Condition_number
If your condition number is ten, then you should expect to lose one digit
of accuracy in your solution, over and above whatever loss of accuracy
comes from the numeric algorithm. A condition number of 64 will lose six
bits, or about 1.8 decimal digits, of accuracy.
If your data starts off with only 1 or 2 digits of accuracy, as in your
example, then the result is meaningless -- the accuracy will be 2-2
digits, or 0 -- *no* digits in the answer can be trusted to be accurate.
I just solved a FEM eigenvalue problem where the condition number of the
mass and stiffness matrices was something like 1e6... Result looked good
to me... So I don't understand what you're saying about 10 = 1 or 2
digits. I think my problem was accurate enough, though I don't know what
error with 1e6 in condition number, I should expect. How did you arrive
at 1 or 2 digits for cond(A)=10, if I may ask ?
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