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Knot Insertion Algorithms for Weighted Splines

In: Proceedings of the Conference on Applied Mathematics and Scientific Computing

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  • Tina Bosner

    (University of Zagreb, Dept. of Mathematics)

Abstract

We develop a technique to calculate with weighted splines of arbitrary order, i.e. with splines from the kernel of the operator D κωD2, with ω piecewisely constant, based on knot insertion type algorithm. The algorithm is a generalization of de Boor algorithm for polynomial splines, and it inserts the evaluation point in the knot sequence with maximal multiplicity. To achieve this, we use a general form of knot insertion matrices, and an Oslo type algorithm for calculating integrals of B-splines in reduced Chebyshev systems. We use the fact that the space of weighted splines is a subspace of the polynomial spline space. The complexity of proposed algorithm can be reduced to the computationally reasonable size. Now we can calculate weighted splines, and the splines associated with their reduced system, in a stable and efficient manner.

Suggested Citation

  • Tina Bosner, 2005. "Knot Insertion Algorithms for Weighted Splines," Springer Books, in: Zlatko Drmač & Miljenko Marušić & Zvonimir Tutek (ed.), Proceedings of the Conference on Applied Mathematics and Scientific Computing, pages 151-160, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-3197-7_9
    DOI: 10.1007/1-4020-3197-1_9
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