Is there more stable mumerical package to calculate the condition number ?

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


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