This paper is devoted to techniques for adaptive spline projection via quasi-interpolation, enabling the efficient approximation of given functions. We employ local least-squares fitting in restricted hierarchical spline spaces to establish novel projection operators for hierarchical splines of degree p. This leads to efficient spline projectors that require $\mathcal{O}(p^d)$ floating point operations and $\mathcal{O}(1)$ evaluations of the given function per degree of freedom, while providing essentially the same accuracy as global approximation. Our spline projectors are based on a unifying framework for quasi-interpolation in hierarchical spline spaces. We present a detailed comparison with the scheme of Speleers and Manni (2016).

本文致力于通过准插值进行自适应样条投影的技术，从而实现给定函数的有效逼近。我们在受限的层次样条空间中采用局部最小二乘拟合，为度p的层次样条建立新颖的投影算子。这导致高效的花键投影仪需要$\mathcal{Ø}（p^d）$ 浮点运算和 $\mathcal{Ø}（\mathrm{1个}）$每个自由度对给定函数的求值，同时提供与全局逼近基本相同的精度。我们的样条投影仪基于统一的框架，用于分层样条空间中的准插值。我们将与Speleers和Manni（2016）的方案进行详细比较。