You can scale your matrix by, say, the inverse of the largest/smallest(nonzero) entry before you compute the norm and use that $\|aM\|=|a|\|M\|$.

And have a look into Higham's book Accuracy and Stability of Numerical Algorrithms to understand how these scalings have an effect on the accuracy.

You can scale your matrix by, say, the inverse of the largest/smallest(nonzero) entry before you compute the norm and use that $\|aM\|=|a|\|M\|$.

And have a look into Higham's book Accuracy and Stability of Numerical Algorithms to understand how these scalings have an effect on the accuracy.