On positivity of principal minors of bivariate Bezier collocation matrix

Abstract

It is well known that the bivariate polynomial interpolation problem at domain points of a triangle is correct. Thus the corresponding interpolation matrix $M$ is nonsingular. L.L. Schumaker stated the conjecture, that the determinant of $M$ is positive. Furthermore, all its principal minors are conjectured to be positive, too. This result would solve the constrained interpolation problem. In this paper, the basic conjecture for the matrix $M$, the conjecture on minors of polynomials for degree <=17 and for some particular configurations of domain points are confirmed.