Multi-degree B-splines

Algorithmic computation and properties

Journal article (2020)

Authors

D. Toshniwal The University of Texas at Austin, Numerical Analysis -

Hendrik Speleers University of Rome Tor Vergata

René R. Hiemstra The University of Texas at Austin

Carla Manni University of Rome Tor Vergata

TJR Hughes The University of Texas at Austin

Research Group

Numerical Analysis () (TU Delft)

B-splines Smooth splines Non-uniform degrees Algorithmic computation Convex partition of unity Linear independence

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http://resolver.tudelft.nl/uuid:3e170312-d5a4-49d5-8787-b69baeefa27b

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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

This paper addresses theoretical considerations behind the algorithmic computation of polynomial multi-degree spline basis functions as presented in Toshniwal et al. (2017). The approach in Toshniwal et al. (2017) breaks from the reliance on computation of integrals recursively for building B-spline-like basis functions that span a given multi-degree spline space. The gains in efficiency are indisputable; however, the theoretical robustness needs to be examined. In this paper, we show that the construction of Toshniwal et al. (2017) yields linearly independent functions with the minimal support property that span the entire multi-degree spline space and form a convex partition of unity.

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