  A simple iterative scheme is proposed for locating the parameter values for
which a 2-parameter family of real symmetric matrices has a double eigenvalue.
The convergence is proved to be quadratic. An extension of the scheme to
complex Hermitian matrices (with 3 parameters) and to location of triple
eigenvalues (5 parameters for real symmetric matrices) is also described.
Algorithm convergence is illustrated in several examples: a real symmetric
family, a complex Hermitian family, a family of matrices with an "avoided
crossing" (no covergence) and a 5-parameter family of real symmetric matrices
with a triple eigenvalue.
