An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition

Abstract EN

A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function.

Given two bivariate spline spaces Smr (Δ) and Snt (Δ) over a domain D with a partition Δ, the Bezout number BN(m,r;n,t;Δ) is defined as the maximum finite number of the common intersection points of two arbitrary piecewise algebraic curves f(x, y)=0 and g(x, y)=0, where f(x, y)∈Smr (Δ) and g(x, y)∈Snt (Δ).

In this paper, an upper bound of the Bezout number for piecewise algebraic curves over a rectangular partition is obtained.