Hello Philippe,
Le 24/05/2018 à 23:20, philippe a écrit :
Le 21/05/2018 à 15:46, Samuel Gougeon a écrit :
There are at least two way to do it :
* either keep *cond([])* to *1* and set all *cond([], p)* to 1 instead
of 0
* or set *cond([])* to *0*.
I don't see any clear reason enforcing a choice rather than the other.
Do you?
from a mathematical point of view the Condition number of a matrix A is
defined by
cond(A)=||A|| . ||A^(-1)||
its interest is that when solving A*x=y rounding errors on y (eps) are
amplified to be cond(A)*eps. The optimal value of cond(A) is 1 (for
identity matrix) so for me it looks natural that cond([])=1 .
I must confess that, unless claiming that *norm([])***is NOT 0, i do
not catch clearly the logical of your conclusion
* /"The optimal value of cond(A) is 1 (for identity matrix) so for me
it looks natural that cond([])=1"/
Indeed, cond([]) = norm([])*norm(inv([])) = 0*norm([]) = 0*0 = 0
By the way, according to the clear explanation you give about the
meaning of the condition number, the value 0 is even more optimal: it
says that small variations are not getting amplified, but killed.
Please let us know more about your proposal for 1 instead of 0.
Regards
Samuel
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