November 9, 2025Open Access

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

Key Points

Approximation using B-spline techniques provides efficient solutions in tensor-product spaces, uncovering new methodologies.
Key findings highlight that local operators yield spline approximations that are fast and computationally easy to achieve.
Application of algorithms for dyadic coarsening operators was assessed in univariate spline spaces on uniform grids with significant results.
Using these methods supports the transition from global computations to local projections, enhancing efficiency.

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.

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

Key Points

Abstract

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