Understanding L2-Norm & Equation: Error Analysis Help

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Homework Help Overview

The discussion revolves around understanding the L2-norm and its application in error analysis, specifically through the equation E(N) = 2*pi ∫ (U(N) - Uexact)² r dr. Participants are exploring the concept of error measurement in relation to approximations and exact values.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are asking for basic explanations of the L2-norm and its significance. There are inquiries about the specific equation's purpose and its relation to the sum of squared errors. Some are considering the application of the L2-norm for calculating a "global" error based on the area between two curves.

Discussion Status

The discussion is ongoing, with participants seeking clarification and exploring different interpretations of the L2-norm and its application. Some guidance has been offered regarding the nature of the L2-norm, but no consensus has been reached on its application to the specific error analysis problem.

Contextual Notes

Participants mention a need for resources and literature on the topic, indicating a potential gap in foundational knowledge. There is also a focus on understanding the implications of the equation provided in the context of error analysis.

mcooper
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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.

Thanks in advance!
 
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What is the difference between this equation and the sum of the errors squared?
 
mcooper said:
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
 
hotvette said:
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.
 

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