Partition of unity systems and B-splines

2014/10/20 by Daniel J. Greenhoe, Greenhoe, Daniel J.
Computer Science · Engineering · Mathematics · #05A10 #41A15 #42C40 #44A35 #46B15 #65D07 #65T60 #Advanced Numerical Analysis Techniques #FOS: Mathematics #General Mathematics (math.GM) #Polynomial and algebraic computation #math.GM #msc:05A10 #msc:41A15 #msc:42C40 #msc:44A35 #msc:46B15 #msc:65D07 #msc:65T60

paper · pdf · doi:10.48550/arxiv.1410.5413

The pdf file was generated with the assistance of XeLaTeX/XeTeX. arXiv admin note: substantial text overlap with arXiv:1410.4859

arxiv created 2014/10/20 · openalex publication_date 2014/10/20 · arxiv updated 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents the basic principles of partition of unity systems and B-splines. Analysis of these systems is performed using Fourier analysis, multi-resolution analysis, and wavelet analysis.

Citations

• On calculating with B-splines
• Properties and applications of transversal operators

Related

• A Tutorial on Uniform B-Spline
• Construction of scaling partitions of unity
• Non-linear Partition of Unity method
• MacMahon's partition analysis XII: Plane partitions
• Splinets -- splines through the Taylor expansion, their support sets and orthogonal bases