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Non-uniform exponential tension splines

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Abstract

We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D 2(D 2–p 2), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C 1, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C 2 tension exponential splines.

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Tina Bosner & Mladen Rogina

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  1. Tina Bosner
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  2. Mladen Rogina
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Correspondence to Tina Bosner.

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Bosner, T., Rogina, M. Non-uniform exponential tension splines. Numer Algor 46, 265–294 (2007). https://doi.org/10.1007/s11075-007-9138-7

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  • DOI: https://doi.org/10.1007/s11075-007-9138-7

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