This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

NormFunction

 NormFunction is an option for functions such as FindFit and NDSolve which gives a function to be minimized in generating results.
• NormFunction->f specifies that should be minimized in generating results.
Find a "best" fit for data using different norms:
The default is to find the best least-squares fit:
Use the 1-norm:
Use a 2-norm for estimating local error in solving an ODE:
Use an -norm:
The error measure makes a difference in the solution quality:
Find a "best" fit for data using different norms:
 Out[1]=
The default is to find the best least-squares fit:
 Out[2]=
 Out[3]=
Use the 1-norm:
 Out[4]=

Use a 2-norm for estimating local error in solving an ODE:
 Out[1]=
Use an -norm:
 Out[2]=
The error measure makes a difference in the solution quality:
 Out[3]=
 Scope   (1)
The norm is used for space and time in PDE solutions:
Plot the actual solution error, when using different error estimation norms:
A plot of the best solution:
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