0
$\begingroup$

if $f(x)=||x||_2^2$ for $ x \in \mathbb{R} $, What is the $2-norm$ relative condition number of $f$ with respect to pertubations of x?

What I have tried:

I have tried the following formula from trefethen book page 131-Numerical Linear Algebra.

enter image description here

I used the 2-norm for: ||J||, ||f(x)||, $||x||$. And my final answer was $\kappa = 2$

My question is. Is this process correct? and how do I know wich norm I have to use for each one of the terms $||J(x)||, ||f(x)|| and ||x||$.

I have these questions because in the same book page 89 and equation (12.3) they state: enter image description here enter image description here

So, I want to know if using the same 2-norm for all the expression is correct and when it is not correct. For instance, in the following example from the same book, page 91 different norms are used.

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.