Understanding L2-Norm & Equation: Error Analysis Help

[mcooper]

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) - U_exact)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.

Thanks in advance!

 

[mcooper]

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

 

[hotvette]

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

 

[mcooper]

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.