Re: Is there more stable mumerical package to calculate the condition number ?
- From: Gordon Sande <g.sande@xxxxxxxxxxxxxxxx>
- Date: Tue, 03 Jul 2007 17:33:30 GMT
On 2007-07-03 14:03:40 -0300, "shna" <nsh1979@xxxxxxxxxxxxx> said:
Hi all.
My problem is to calculate the condition number of arbitrary matrix A.
When the largest eigenvalue and the smallest eigenvalue of A are given by
lam_max and lam_min, the condition number is defined as
lam_max / lam_min
I hope to get a numerical package to condition number of the matrix A, with
high relability.
In fact, I have developed the procedure to add perturbation of A to increase
the condition number of A continuously.
(This is from some other experimental issue.)
Given the procedure, I want to plot the graph how fast the condition number
increased. This is why I require a numerical package.
Along this issue, now, I am calculating the condition number by using SVD or
Eigen-decomposition which LAPACK provides. However, I found that the
condinum number is not anymore increased when it becomes more than 10^20 or
10^30. So, it makes my major concern, whether or not using such SVD and
eigen-decomposition can cover the extreme situation, even when the condinum
number is more than 10^100 or 10^200.
Of course, this result may be not due to limitation of LAPACK, but due to
the problem of my developed procedure.
Normally, do you think that there is the numerical limitation of algorithm
to calculate the condition number ?
Then, do you have idea to the condition number more accurately, even though
the condition number is very lage
or know the related package ?
And, is such numerical package in LAPACK ?
Thank you.
From Seung-Hoon Na
If the largest floating poinnt number is 10^38 (as is common) then observing
a reported condition number larger than 10^38 would be "difficult". You
would have to use other than the normal hardwre number representations.
Even having the largest eigenvalue exceed 10^38 would prove to be difficult.
There seems to be a disconnect between wanting to use existing software that
uses ordinary computer arithmetic and observing derived quantities which
are outside the range of that arithmetic. Perhaps you just forgot to say
how you are addressing this technical awkwardness.
.
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