[EM] Re: mathematical norms (Stephane Rouillon)

[Olli Salmi]

>The norm-1 is the sum of the absolute values of the differences between the
>values in each set for every elements. L1 = (for i=1 to n) Sigma |Xi-Si|.
>The norm-2 is the square root of the sum of the squares of the differences
>between the values in each set for every elements. L2 = sqrt( (for i=1 to n)
>Sigma (Xi-Si)^2).
>The least square method minimizes norm L2.
>The norm-N is L(N)= ( (for i=1 to n) Sigma (Xi-Si)^N)^(1/N).
>The infinite norm is the limit of norm-N when N tends to infinite: Linf =
>(over i) max {|Xi-Si|}.

Thanks. This is useful.

>A basic example: the Hockey pool.
>Let's try to predict the number of points some fictional players will make
>next year:
>Player            Prediction            Reality
>Gretzky                     99                     0
>Saku Koivu               11                   32
>Mario Lemieux          66                   78

It's a pity you couldn't give more fictional points to Saku Koivu. It 
must have been because he was fighting with his disease.

>All this to say that from what I understood, Sainte-Lague minimizes norm L1
>and not norm L2 as Olli said...

It seems to be what I was saying.

Olli Salmi