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Near-optimal tension parameters in convexity preserving interpolation by generalized cubic splines

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Abstract

We offer the algorithm for choosing tension parameters of the generalized splines for convexity preserving interpolation. The resulting spline minimally differs from the classical cubic spline and coincides with it if sufficient convexity conditions are satisfied for the last one. We consider specific algorithms for different generalized cubic splines such as rational, exponential, variable power, hyperbolic splines, and splines with additional knots.

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Acknowledgments

We would like to thank the referees for their useful suggestions and comments that, with no doubt, have helped to improve the quality of this paper.

Funding

This work was financially supported by the program of fundamental scientific researches of the SB RAS (Project No. 0314-2019-0013).

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  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Vladimir V. Bogdanov & Yuriy S. Volkov

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  1. Vladimir V. Bogdanov
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Correspondence to Yuriy S. Volkov.

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Bogdanov, V.V., Volkov, Y.S. Near-optimal tension parameters in convexity preserving interpolation by generalized cubic splines. Numer Algor 86, 833–861 (2021). https://doi.org/10.1007/s11075-020-00914-9

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