In this paper, optimal matrix adjustment was examined with a focus on connectivity and its preservation. To accomplish this, techniques which do not preserve the sparsity pattern were applied in an iterative approach that forces the preservation of the zero/nonzero pattern of the original stiffness matrix. This approach showed impressive results for locating damaged truss members. In addition, this approach also provides understanding of optimal updates in general.
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Suzanne Smith (1992) studied this question.