engleski

Knot Insertion Algorithms for Weighted Splines

We develop a technique to calculate with weighted splines of arbitrary order, i.e. with splines from the kernel of the operator D^kwD^2, with w 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.

Chebyshev system; weighted spline; knot insertion; de Boor algorithm; Oslo

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