  We compare two established and a new method for the calculation of spectral
bounds for Hessian matrices on hyperrectangles by applying them to a large
collection of 1522 objective and constraint functions extracted from benchmark
global optimization problems. Both the tightness of the spectral bounds and the
computational effort are assessed. Specifically, we compare eigenvalue bounds
obtained with the interval variant of Gershgorin's circle criterion [2,6],
Hertz and Rohn's [7,16] method for tight bounds of interval matrices, and a
recently proposed Hessian matrix eigenvalue arithmetic [12], which deliberately
avoids the computation of interval Hessians.
