Computing Most Nearly Rank-Reducing Structured Matrix Perturbations

Abstract
The paper investigates the problem of computing structured matrix perturbations that cause, or most nearly cause, some specified system matrix to fail to have full rank. The paper discusses some theoretical issues concerning the existence of solutions to these problems. It suggests a numerical approach to computing solutions that utilizes some ideas on differentiation of singular values. Finally, an algorithm for finding structured most rank-reducing perturbations and structured most nearly rank-reducing perturbations is developed. The paper demonstrates convergence of the algorithm to a rank-reducing perturbation or to a local minimum for a most nearly rank-reducing perturbation. Numerical examples illustrating the technique are included.

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