On k-Monotone Approximation by Free Knot Splines

@article{Kopotun2003OnKA,
  title={On k-Monotone Approximation by Free Knot Splines},
  author={Kirill Kopotun and Alexei Shadrin},
  journal={SIAM J. Math. Analysis},
  year={2003},
  volume={34},
  pages={901-924}
}
Let SN,r be the (nonlinear) space of free knot splines of degree r − 1 with at most N pieces in [a, b], and let M be the class of all k-monotone functions on (a, b), i.e., those functions f for which the kth divided difference [x0, . . . , xk]f is nonnegative for all choices of (k+1) distinct points x0, . . . , xk in (a, b). In this paper, we solve the problem of shape preserving approximation of k-monotone functions by splines from SN,r in the Lp-metric, i.e., by splines which are constrained… CONTINUE READING