On computing the generalized Crawford number of a matrix

We use methods of geometric computing combined with hermitean matrix eigenvalue/eigenvector evaluations to find the generalized Crawford number of a pair of hermitean matrices S1 and S2 quickly and to high precision. The classical Crawford number is defined as the minimal distance from zero in C to the field of values of the associated complex matrix A=S1+iS2 if zero lies outside the field of values of A. We describe, test, and compare a geometry based MATLAB code for finding for the generalized Crawford number that measures the smallest distance of zero from the boundary of the field of values of A even if zero lies inside.