A companion matrix resultant for Bernstein polynomials Original Research Article

A closed form expression for a companion matrix M of a Bernstein polynomial is obtained, and this is used to derive an expression for a resultant matrix of two Bernstein polynomials. It is shown that M differs from its equivalent form for a power basis polynomial because an upper triangular Hankel matrix does not define a similarity transformation between M and MT. A measure of the numerical condition of a resultant matrix, for polynomials in an arbitrary basis, is reviewed and this is used to compare the stability of two resultant matrices. In particular, computational tests are performed and it is shown that the resultant matrix of two Bernstein polynomials is numerically better conditioned than the resultant matrix that is obtained when a simple parameter substitution is used to transform the polynomials to the power basis.