  La Budde's method computes the characteristic polynomial of a real matrix A
in two stages: first it applies orthogonal similarity transformations to reduce
A to upper Hessenberg form H, and second it computes the characteristic
polynomial of H from characteristic polynomials of leading principal
submatrices of H. If A is symmetric, then H is symmetric tridiagonal, and La
Budde's method simplifies to the Sturm sequence method. If A is diagonal then
La Budde's method reduces to the Summation Algorithm, a Horner-like scheme used
by the MATLAB function POLY to compute characteristic polynomials from
eigenvalues. We present recursions to compute the individual coefficients of
the characteristic polynomial in the second stage of La Budde's method, and
derive running error bounds for symmetric and nonsymmetric matrices. We also
show that La Budde's method can be more accurate than POLY, especially for
indefinite and nonsymmetric matrices A. Unlike POLY, La Budde's method is not
affected by illconditioning of eigenvalues, requires only real arithmetic, and
allows the computation of individual coefficients.
