Interlacing property for B-splines

Authors:
Simon Foucart
Affiliations:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
Venue:
Journal of Approximation Theory
Year:
2005

Citing 3
Cited 0

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New upper bound for the B-spline basis condition number, II: a proof of de Boor's 2k-conjecture

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Markov interlacing property for perfect splines

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Abstract

we prove that the zeros of the derivatives of any order of a B-spline are increasing functions of its interior knots. We then prove that if the interior knots of two B-splines interlace, then the zeros of their derivatives of any order also interlace. The same results are obtained for Chebyshevian B-splines.