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

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 specif...

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Bibliographic Details
Published inNumerical algorithms Vol. 86; no. 2; pp. 833 - 861
Main Authors Bogdanov, Vladimir V., Volkov, Yuriy S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2021
Springer Nature B.V
Subjects
Algebra
Algorithms
Computer Science
Convexity
Inheritances
Interpolation
Numeric Computing
Numerical Analysis
Original Paper
Parameters
Theory of Computation
Generalized cubic spline
Tension parameters
Sufficient conditions of convexity
Convex interpolation
65D05
65D17
Algorithm
65D07
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00914-9