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Diagonal Perturbations of Linear Equations

  1. Nov 6, 2012 #1
    Consider the system of linear equations (A+D)x=b, where D is a positive semidefinite diagonal matrix. Assume for simplicity that (A+D) is full rank for any D that we care about. In my particular case of interest, D has the form D = blkdiag(0,M) for some positive diagonal matrix M. So, a subset of the diagonal entries of A are being perturbed.

    Are there any off-the-shelf theorems that characterize how the components of the solution x change as the elements of D change? Intuitively as M increases in size, the bottom elements of x should shrink. Coupling through off-diagonal elements of A should then also shrink the top elements a little bit.

  2. jcsd
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