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Soize uncertainty/randomness problem

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Following a maximization of the entropy, Soize obtained that random mass, stiffness, and damping matrices would involve a positive definite random matrix G, expressed in Cholesky form

    G = LLT

    where L is a lower triangular matrix. All elements of L are independent of each other, which allows the determination of the moments of G.

    It is desired to compute the mean and second moment of G-1 for a 2X2 matrix G in terms of appropriate moments of the random elements of L. Note: off-diagonal elements of L are zero mean random variables (Gaussian) and the diagonal elements of L are positive only.

    2. Relevant equations

    In general for 1D:

    E[X] = μx
    E[X2] = σ2 + μx2
    E[(X-μx)2] = σx2



    3. The attempt at a solution
    Compute G-1:

    G = LLT

    G-1 = (LT)-1(L)-1

    G-1 = (L-1)T(L-1)

    My assumption is that I'm trying to find the moments, mean and second, for L11, L21 and L22, the elements of the lower triangle of G-1 which is a 2X2 matrix.

    I have no definition for L at this time. I'm still looking in research papers. How should I approach the problem? Thanks in advance for any suggestions.
     
    Last edited: Apr 11, 2012
  2. jcsd
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