NormFunction

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is an option for functions such as FindFit and NDSolve which gives a function to be minimized in generating results.

Details

NormFunction->f specifies that f[data] should be minimized in generating results.

Examples

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Basic Examples (2)Summary of the most common use cases

Find a "best" fit for data using different norms:

In[1]:=1

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https://wolfram.com/xid/0en0w2qvm-o3pvv

Out[1]=1

The default is to find the best least-squares fit:

In[2]:=2

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https://wolfram.com/xid/0en0w2qvm-ch1c6

Out[2]=2

Use the -norm instead:

In[3]:=3

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https://wolfram.com/xid/0en0w2qvm-hl628z

Out[3]=3

Use the 1-norm:

In[4]:=4

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https://wolfram.com/xid/0en0w2qvm-iplfr

Out[4]=4

Use a 2-norm for estimating local error in solving an ODE:

In[1]:=1

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https://wolfram.com/xid/0en0w2qvm-gudy8y

Out[1]=1

Use an -norm:

In[2]:=2

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https://wolfram.com/xid/0en0w2qvm-j54nkp

Out[2]=2

The error measure makes a difference in the solution quality:

In[3]:=3

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https://wolfram.com/xid/0en0w2qvm-m1j0ck

Out[3]=3

Scope (1)Survey of the scope of standard use cases

The norm is used for space and time in PDE solutions:

In[1]:=1

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https://wolfram.com/xid/0en0w2qvm-f8j0t

Plot the actual solution error, when using different error estimation norms:

In[2]:=2

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https://wolfram.com/xid/0en0w2qvm-bt6wo5

Out[2]=2

A plot of the best solution:

In[3]:=3

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https://wolfram.com/xid/0en0w2qvm-hrtl9l

Out[3]=3

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