On positivity of principal minors of bivariate Bezier collocation matrix
Presented by Mr. Tadej KANDUč
Type: Oral presentation
In approximation theory, 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 and all principal minors of M are positive. This result would solve the constrained interpolation problem. In this talk, 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.