On positivity of principal minors of bivariate Bezier collocation matrix
arXiv:1106.0631 · doi:10.1016/j.amc.2013.11.034
Abstract
It is well known that the bivariate polynomial interpolation problem at domain points of a triangle is correct. Thus the corresponding interpolation matrix is nonsingular. L.L. Schumaker stated the conjecture, that the determinant of 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 , the conjecture on minors of polynomials for degree <=17 and for some particular configurations of domain points are confirmed.