This article describes an elementary construction of a dual basis for nonuniform B-splines that is local, $$L^\infty $$ L ∞ -stable, and reproduces polynomials of any prescribed degree. This allows one to define local projection operators with near-optimal approximation properties in any $$L^q$$ L q , $$1 \le q \le \infty $$ 1 ≤ q ≤ ∞ , and high order moment preserving properties. As the dual basis functions share the same piecewise polynomial structure as the underlying splines, simple quadrature formulas can be used to compute the projected spline coefficients.

中文翻译：

---

矩保持局部样条投影算子

本文描述了局部非均匀 B 样条的对偶基础的基本构造，$$L^\infty $$ L ∞ -稳定，并再现任何规定次数的多项式。这允许我们在任何 $$L^q$$ L q 、$$1 \le q \le \infty $$ 1 ≤ q ≤ ∞ 和高阶矩保持性质中定义具有接近最优近似属性的局部投影算子。由于双基函数与底层样条共享相同的分段多项式结构，因此可以使用简单的求积公式来计算投影样条系数。