Further lower bounds for the smallest singular value

In an earlier paper of the first author, Gersgorin's theorem was used in a novel way to give a simple lower bound for the smallest singular value of a general complex matrix. That lower bound was stronger than previous published bounds. Here, we use three variants of Gersgorin's theorem in a similar way to give further lower bounds. Each of the new bounds is more complicated, but generally stronger, than the pure Gersgorin-based bound. The three new bounds are mutually noncomparable. (C) 1998 Elsevier Science Inc.