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Weird Sum of Squares as a Vector Norm and Gauss-Newton optimization

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    A([itex]\vec{x}[/itex]) = (F + T * x )2

    F is a constant,
    x is a 2×1 vector
    T is a (constant) 1×2 matrix


    B([itex]\vec{x}[/itex]) = || K.Z.x ||2 k:3[itex]\times[/itex]3 matrix and Z:3[itex]\times[/itex]2, x the same as above


    B(x) is also R2→R


    C(x) = A(x) + B(x)

    2. Relevant equations

    1- I am confused how can (A + B) be represented as a (vector) norm like this:

    C(x) = || (F , 0) + (T , K).Z.x ||2

    , i.e., what would be the dimensionality and meaning of the matrix (T , K) ? (discrepancy between the first 1 [itex]\times[/itex] 2 entry and second 3 [itex]\times[/itex] 3?)

    3. The attempt at a solution
     
    Last edited: Apr 18, 2012
  2. jcsd
  3. Apr 20, 2012 #2
    No solution?:frown:
     
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