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L1,L2,L_infinity error

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Old   March 21, 2013, 22:18
Question L1,L2,L_infinity error
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Hi, I am confused with the definition of the three errors. Are they defined as follows?
L1 = sum(abs(uex-u))*dx;
L2 = sqrt(dx*sum((uex-u)^2));
L_infinity = max(abs(uex-u));

Is L_infinity always larger than the other two errors?

Last edited by Wenjun; March 21, 2013 at 22:20. Reason: typo
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Old   March 22, 2013, 05:26
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Filippo Maria Denaro
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Quote:
Originally Posted by Wenjun View Post
Hi, I am confused with the definition of the three errors. Are they defined as follows?
L1 = sum(abs(uex-u))*dx;
L2 = sqrt(dx*sum((uex-u)^2));
L_infinity = max(abs(uex-u));

Is L_infinity always larger than the other two errors?
First, a general Lp operator is called Holder norm, it applies on a vector in the discrete case, in your example, the error is the difference (uex-u), not the norm.
Then, you can define the norm in average or not, you can find some useful note in the book of LeVeque or any other book on numerical analysis.
L_infinity becomes the more restrictive
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Old   March 22, 2013, 05:31
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Ok , thanks for your advice!
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