Abstract
Given m square matrices A/sub 1/, ..., A/sub m/, let A denote the set of all their convex combinations. Then the authors consider the problem of determining a member of A whose minimum singular value is the smallest. A related problem, known as robust nonsingularity problem, is to determine if every member of A is nonsingular. Clearly a solution to the authors' problem automatically solves the robust nonsingularity problem. Unfortunately, the robust nonsingularity problem has been demonstrated to be NP-hard which in turn makes the authors' problem NP-hard. To avoid this computational intractability, the authors provide an algorithm that computes a lower bound and an upper bound on the least minimum singular value within a prescribed tolerance. Of course, if the prescribed tolerance is set to zero then the authors' algorithm would compute the least minimum singular value. The authors' method makes use of the so-called simplicial algorithms. >
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