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Least absolute minimization

  1. Feb 23, 2006 #1
    Hello,


    I have been having problems finding the way to minimize the sum of absolute values. Specificaly im looking for the value of X that will minimize the sum|Xi-V|<-- i=1,....n . I know that V should be equal to the mean value of X. But I do not know the correct aproach to finding this minimum.

    Can I square the Xi-V and differentiate? or is there another approach?

    Thanks....
     
  2. jcsd
  3. Feb 23, 2006 #2

    0rthodontist

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    So is Xi X times i?
     
  4. Feb 23, 2006 #3
    Sorry about that,

    i---> is the sub index. Meaning X1....Xn.

    Then it is Sum from i={1 to n }of |Xi-V|.
     
  5. Feb 23, 2006 #4

    0rthodontist

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    Well then that expression is completely independent of the value of X. Do you mean you are looking for a V to minimize that expression? If you are then you can let V be any value between X(n/2) and X(n/2+1) if n is even, and you can let V be X((n+1)/2) if n is odd.
     
    Last edited: Feb 23, 2006
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