Understanding L2-Norm & Equation: Error Analysis Help

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The L2-norm is a mathematical concept representing the length of a vector, akin to the Pythagorean theorem. In the context of error analysis, the equation E(N) = 2*pi ∫ (U(N) - Uexact)² r dr calculates the error between an approximation and an exact value by integrating the squared differences over a specified range. This approach provides a "global" error measurement, which is useful for assessing the accuracy of solutions. The discussion also highlights the need for resources to better understand these concepts and their applications in error analysis. Overall, the L2-norm can indeed be applied to evaluate the area between curves in this context.
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.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
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