engleski

On calculating with lower order Chebyshev splines

We develop a technique to calculate with Chebyshev Splines of orders $3$ and $4$, based on the known derivative formula for Chebyshev splines and an Oslo type algorithm. We assume that splines in the reduced system are simple enough to calculate. Local bases of Chebyshev splines of order $3$ and $4$ can thus be evaluated as positive linear combinations of less smooth Chebyshev B-splines. The coefficients in such linear combinations are discrete Chebyshev splines, normalized so as to make a partition of unity. There are a number of interesting special cases, such as Foley's $\nu$-splines, Chebyshev polynomial splines ($q$-splines), and splines in tension which can be calculated stably by such formul\ae.

spline; Chebyshev system; recurrence

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