engleski

Stable Algorithm for Calculating with Q-splines

We are using a technique to calculate with Tchebycheffian splines of order $\le 4$, based on the known derivative formula for Tchebycheffian splines and Oslo type algorithm, to produce simple formul\ae for qB-splines developed by Kulkarni and Laurent. Starting with the known fact that local basis for $q$-splines of order 3 and 4 can be evaluated by making positive linear combinations of less smooth, one order higher polynomial B-splines, we deduce a simple and stable algorithm for such splines. It is an interesting fact in itself, that the coefficients in such linear combinations are discrete Tchebycheffian splines, and therefore make a partition of unity. The same is true for qB-splines themselves.

T-spline; Q-spline; Knot insertion

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