A resultant matrix for scaled Bernstein polynomials

The established theory of the resultant of two polynomials assumes that the y are expressed in the power (monomial) basis, and a basis transformation i s therefore necessary if thr, resultant of two Bernstein polynomials is req uired. In this paper, a resultant matrix for two scaled Bernstein polynomia ls (polynomials of degree n whose basis functions are (1 - x)(n-i)x(i), 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 resultan t matrix s(M), where s(x) is a scaled Bernstein polynomial. (C) 2000 Elsevi er Science Inc. All rights reserved. AMS classification: 11C08; 11C20.