engleski

Knot insertion algorithms for Chebyshev splines

In this thesis our point of interest are canonical complete Chebyshev (CCC)– systems and splines associated with them. We are interested in finding numerically stable algorithms for calculating with such splines, and we do that by generalizing the knot insertion based algorithms for polynomial splines to CCC– systems. To be able to construct these algorithms, we introduce knot insertion matrices, and then develop Oslo type algorithms and generalized de Boor algorithm. To show the practical value of these algorithms, we apply them on four kinds of splines: weighted, qsplines, tension and cycloidal splines. Weighted and tension splines are particulary interesting, since weighted are the only splines which can be calculated for the order higher than 4, and tension splines because they have the most wide application. For each of these splines, algorithms are developed with all the details specific for the spline in question. Finally to illustrate the practical computer use of given algorithms, we list program codes involved in calculating with C1 and C2 tension splines.

Spline ; Knot insertion ; Chebyshev systems

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