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Locally optimal knots and tension parameters for exponential splines. (English) Zbl 1098.65010
Summary: Tension can be applied to cubic splines in order to avoid undesired spurious oscillations. This leads to the well-known (exponential) spline in tension. It is crucial but unfortunately difficult to find suitable tension parameters of interpolating splines in tension. Instead of heuristics, we propose a simultaneous knot placing and tension setting algorithm for least-squares splines in tension which includes interpolating splines in tension as a special case. Moreover, the splines presented here are the foundation of exponential surface splines on fairly arbitrary meshes [cf. K. O. Riedel, ZAMM Z. Angew. Math. Mech. 85, No. 3, 176–188 (2005; Zbl 1067.65017)].
Reviewer: Reviewer (Berlin)

##### MSC:
 65D07 Numerical computation using splines 65D10 Numerical smoothing, curve fitting 65D05 Numerical interpolation 41A15 Spline approximation
##### Software:
FITPACK; pchip; TSPACK
Full Text:
##### References:
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