On positivity of principal minors of bivariate Bezier collocation matrix

Details On positivity of principal minors of bivariate Bezier collocation matrix On positivity of principal minors of bivariate Bezier collocation matrix

2011-06-03

arxiv.org/abs/1106.0631v1

Mathematics

Numerical Analysis

Scientific paper

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.

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