engleski

Evaluation of tension splines

Tension spline of order $k$ is a function that, for a given partition $x_0<ldots <x_n$, on each interval $[x_, x_{;i+1};]$ satisfies differential equation $(D^k- ho_i^2D^{;k-2};)u=0$, where $ ho_i$'s are prescribed nonnegative real numbers. Most articles deal with tension splines of order four, applied to the problem of convex (or monotone) interpolation or to the two-point boundary value problem for ODE. Higher order tension splines are desribed in several papers, but no application is given. Possible reason for this is a lack of an appropriate algorithm for their evaluation. Here we present an explicit algorithm for evaluation of tension splines of arbitrary order. We especially consider stable and accurate computation of hyperbolic-like functions used in our algorithm.

Tension spline; B-spline; evaluation

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