In this article, we study dyadic coarsening operators in univariate spline spaces and in tensor-product spline spaces over uniform grids. Our construction is strongly motivated by the work of Bartels, Golub, and Samavati (2006), Some observations on local least squares, BIT, 46(3):455--477. The proposed operators are local in nature and yield approximations to a given spline that are comparable to the global L2-best approximation, while being significantly faster to compute and computationally inexpensive.

翻译：本文研究均匀网格上一元样条空间及张量积样条空间中的二进粗化算子。我们的构造主要受Bartels、Golub与Samavati（2006）在《BIT》期刊第46卷第3期455-477页发表的《关于局部最小二乘法的若干观察》工作的启发。所提出的算子具有局部特性，能够生成与全局L2最佳逼近相当的给定样条逼近，同时计算速度显著更快且计算成本低廉。