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L2 - norm

  1. Mar 6, 2010 #1
    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 [tex]\int[/tex] (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.

    Thanks in advance!
     
  2. jcsd
  3. Mar 7, 2010 #2
    What is the difference between this equation and the sum of the errors squared?
     
  4. Mar 7, 2010 #3

    hotvette

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

    http://mathworld.wolfram.com/L2-Norm.html
     
  5. Mar 11, 2010 #4
    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.
     
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