Bivariate semialgebraic splines

JOURNAL OF APPROXIMATION THEORY

卷:254

Article

DiPasquale, Michael¹  Sottile, Frank² 

[1] Colorado State Univ, Dept Math, Ft Collins, CO 80521 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Spline modules;    Dimension of spline spaces;    Hilbert function;    Hilbert polynomial;   

DOI  :  10.1016/j.jat.2020.105392

来源: Elsevier

【 摘 要 】

Semialgebraic splines are bivariate splines over meshes whose edges are arcs of algebraic curves. They were first considered by Wang, Chui, and Stiller. We compute the dimension of the space of semialgebraic splines in two extreme cases. If the polynomials defining the edges span a three-dimensional space of polynomials, then we compute the dimensions from the dimensions for a corresponding rectilinear mesh. If the mesh is sufficiently generic, we give a formula for the dimension of the spline space valid in large degree and bound how large the degree must be for the formula to hold. We also study the dimension of the spline space in examples which do not satisfy either extreme. The results are derived using commutative and homological algebra. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free