Left Inverses for B-spline Subdivision Matrices in Tensor-Product Spaces

Abstract: 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.