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