This book considers structure preserving matrix methods for computations
on Bernstein polynomials whose coefficients are corrupted by noise. The
ill-posed operations of greatest common divisor computations and
polynomial division are considered, and it is shown that structure
preserving matrix methods yield excellent results. With respect to
greatest common divisor computations, the most difficult part is the
computation of its degree, and several methods for its determination are
presented. These are based on the Sylvester resultant matrix, and it is
shown that a modified form of the Sylvester resultant matrix yields the
best results. The B´ezout resultant matrix is also considered, and it is
shown that the results from it are inferior to those from the Sylvester
resultant matrix.