An upper bound of the Bézout number for piecewise algebraic curves over a rectangular partition
Summary: A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces \(S^r_m(\Delta)\) and \(S^t_n(\Delta)\) over a domain \(D\) with a partition \(\Delta\), the Bézout number BN\((m, r; n, t; \Delta )\) 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 \(f(x, y) \in S^r_m(\Delta)\) and \(g(x, y) \in S^t_n(\Delta)\). In this paper, an upper bound of the Bézout number for piecewise algebraic curves over a rectangular partition is obtained.
scientific article; zbMATH DE number 6093825