Anup,
I wanted to know the condition number of my system_matrix and hence I have
used the line in blue (below) in my CG solve function.
It shows the condition number. But in the documentation the definition of this
is not mentioned.
You mean the documentation is missing a definition of what the condition
number is?
I mean when I store
my system matrix and calculate its max and min eigenvalues in matlab and then
calculate the condition number as their ratio
(i.e, max_eigen_val/ min_eigen_val), this does not match with the one
calculated by connect_condition_number_slot.
The quantities differ by two order of magnitudes.
Which norm does Matlab use to define the condition number? And are you using a
preconditioner when calling CG?
What CG can only provide you with is an *estimate* of the condition number of
the (preconditioned) matrix. It does not actually compute the min and max
eigenvalues, but gets the estimate for the condition number by computing the
eigenvalues of the subspace in which it finds the current approximation. These
estimates converge to the true condition number if you just take enough
iterations, but you may also be stopping the iteration too quickly.
Best
Wolfgang
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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