Understanding the L2-Norm and its Equation

[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...

E(N) = 2*pi$$\int$$(u(N) - u_exact)² r dr

Where E is the error for a specific N. 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.

 

[BSCowboy]

I know of $$l_p$$ spaces. For $$0\leq p<\infty$$ it's the set whose elements are sequences of scalars $$x=\{\lambda_1, \lambda_2, \ldots, \lambda_n,\ldots\}$$ such that $$\left(\sum|\lambda_n|^p\right)^{\frac{1}{p}}$$ is convergent.

But, I can't really help you with your problem.

 

[mathman]

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...

E(N) = 2*pi$$\int$$(u(N) - u_exact)² r dr

Where E is the error for a specific N. 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.

L2 norm (general) is the square root of the integral of the square of the absolute value of the function.

Your specific equation is for the variance (square of L2 norm, centered at the mean) of some random variable u(N). It looks like it is two dimensional, expressed in polar coordinates, where u(N) is independent of angle.