Optimal Gerschgorin-type inclusion intervals of singular values

In this paper, some optimal inclusion intervals of matrix singular values are discussed in the set A of matrices equimodular with matrix A. These intervals can be obtained by extensions of the Gerschgorintype theorem for singular values, based only on the use of positive scale vectors and their intersections. Theoretic analysis and numerical examples show that upper bounds of these intervals are optimal in some cases and lower bounds may be non-trivial (i.e. positive) when PA is a H -matrix, where P is a permutation matrix, which improves the conjecture in Reference (Linear Algebra Appl. 1984; 56:105–119). Copyright q 2006 John Wiley & Sons, Ltd.