%0 Journal Article
%T On positivity of principal minors of bivariate Bezier collocation matrix
%A Gasper Jaklic
%A Tadej Kanduc
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1106.0631v2