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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

Thanks

-John

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# Diagonal Perturbations of Linear Equations

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