论文信息 - Interlacing property for B-splines

Interlacing property for B-splines

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.

Simon Foucart

[1] C. Chui,et al. Approximation theory X : abstract and classical analysis , 2002 .

[2] Günter W. Mühlbach. A recurrence relation for generalized divided differences with respect to ECT-systems , 2004, Numerical Algorithms.

[3] G. Nürnberger. Approximation by Spline Functions , 1989 .

[4] B. Sahakian,et al. Spline Functions and Multivariate Interpolations , 1993 .

[5] B. Bojanov,et al. Exact Markov-Type Inequalities for Oscillating Perfect Splines , 2001 .

[6] Interpolation with lagrange polynomials a simple proof of Markov inequality and some of its generalizations , 1992 .

[7] Guido Walz,et al. On the Chebyshev Norm of Polynomial B-Splines , 1995 .

[8] Karl Scherer,et al. New Upper Bound for the B-Spline Basis Condition Number , 1999 .

[9] B. Bojanov. Markov interlacing property for perfect splines , 1999 .