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Consider the system of linear equations (A+D)x=b, where D is a positive semidefinite diagonal matrix. 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? Assuming you don't lose full rank, intuitively as M increases in size, the bottom elements of x should shrink. Coupling through A should then also shrink the top elements a little bit.

Thanks -John

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    Do we know anything about the matrix A?2012-11-06
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    It's full rank and indefinite, so for arbitrary D as I've written it, the matrix A+D is potentially singular. But let's say we restrict our attention to sufficiently small or large D such that this isn't a problem.2012-11-06

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