On the condition of cubic B-splines

Uniform stability is a key property of B-spline bases, but so far, sharp bounds on the condition number have been available only for degrees ≤2. Relying on computer algebra to perform the rather elaborate computations, we derive the lowest upper bound on the condition number of cubic B-splines and p...

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Bibliographic Details
Published in:Journal of approximation theory 2023-05, Vol.289, p.105883, Article 105883
Main Authors: Lyche, Tom, Mørken, Knut, Reif, Ulrich
Format: Article
Language:English
Subjects:
B-spline
Condition number
Stability
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Summary:Uniform stability is a key property of B-spline bases, but so far, sharp bounds on the condition number have been available only for degrees ≤2. Relying on computer algebra to perform the rather elaborate computations, we derive the lowest upper bound on the condition number of cubic B-splines and present a conjecture concerning the according value for the quartic case.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2023.105883