Abstract:

With constructive algebraic geometric tools, the authors have verified that a Lower set S associated with a Cartesian subset of an arbitrary 2-dimensional node set P must be contained in two special Lower sets S_x(P) and S_y(P), and proposed a criterion for judging whether the polynomial space determined by S_x(P) or S_y(P) is an interpolation space of minimal degree for the Lagrange interpolation on P.

Key words: bivariate Lagrange interpolation, Lower set, Cartesian set, interpolation space of minimal degree