Abstract
Letx v =cos (πν/n) (v=0, 1, …,n). It is shown that theB-splineM(x)=M(x; x 0 ,x 1 ,…, x n ) is such thatM (n)n (x) has a constant absolute value (=2n−2 (n−1)!) in [−1, 1]. Its integralf 0(x)=∫ x−1 M(t)dt is shown to have an optimal property that allows to solveexplicitly a certain time-optimal control problem.
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Schoenberg, I.J. The perfectB-splines and a time-optimal control problem. Israel J. Math. 10, 261–274 (1971). https://doi.org/10.1007/BF02771643
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DOI: https://doi.org/10.1007/BF02771643