Eigenvalue location for nonnegative and Z-matrices

Let L-0(k) denote the class of n x n Z-matrices A = tI - B with B greater than or equal to 0 and rho(B) less than or equal to t < rho(k+1)(B), where rho(k), (B) denotes the maximum spectral radius of k x k principal submatrices of B. Bounds are determined on the number of eigenvalues with positive real parts for A is an element of L-0(k), where ii satisfies, [n/2] less than or equal to k less than or equal to n - 1. For these classes, when k = ii - 1 and n - 2, wedges are identified that contain only the unique negative eigenvalue of A. These results lead to new eigenvalue location regions for nonnegative matrices; (C) 1998 Elsevier Science Inc. All rights reserved.