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 present a conjecture concerning the according value for the quartic case.(c) 2023 Elsevier Inc. All rights reserved.