# L2 - norm

Could someone please explain to me in fairly basic terms what the L2-norm is and what it does please. More specifically let me know what the following equation does, if possible...

E(N) = 2*pi $$\int$$ (U(N) - Uexact)2 r dr

Where E is the error for a specific N. Ultimately I have values for an approximation and exact values and want to do some sort of error analysis.

I haven't found any good resources for learning about this on the internet. Also if someone could recommend a good book that would be great.

## Answers and Replies

What is the difference between this equation and the sum of the errors squared?

hotvette
Homework Helper
Could someone please explain to me in fairly basic terms what the L2-norm is and what it does please

The L2 norm is the length of a vector. Think Pythagorean theorem.

http://mathworld.wolfram.com/L2-Norm.html

The L2 norm is the length of a vector. Think Pythagorean theorem.

Hi, thanks for your reply. I am in need of something that will give me a "global" error of an solution that I have. I have a plot of the approximation against the exact value and I am guessing I need to calculate the area between the 2 curves (hence the equation in the 1st post?). Can the L2 norm be applied here?

Your responses are much appreciated.