A resultant matrix for scaled Bernstein polynomials Original Research Article

The established theory of the resultant of two polynomials assumes that they are expressed in the power (monomial) basis, and a basis transformation is therefore necessary if the resultant of two Bernstein polynomials is required. In this paper, a resultant matrix for two scaled Bernstein polynomials (polynomials of degree n whose basis functions are (1−x)n−ixi, i=0,…,n) is constructed. In particular, a companion matrix M for a scaled Bernstein polynomial r(x) is developed, and this is used to form a resultant matrix s(M), where s(x) is a scaled Bernstein polynomial.