Univariate cubic \(L_1\) interpolating splines: analytical results for linearity, convexity and oscillation on 5-pointwindows (Q1662554)
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scientific article; zbMATH DE number 6920525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Univariate cubic \(L_1\) interpolating splines: analytical results for linearity, convexity and oscillation on 5-pointwindows |
scientific article; zbMATH DE number 6920525 |
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Univariate cubic \(L_1\) interpolating splines: analytical results for linearity, convexity and oscillation on 5-pointwindows (English)
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20 August 2018
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Summary: We analytically investigate univariate \(C^1\) continuous cubic \(L_1\) interpolating splines calculated by minimizing an \(L_1\) spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting \(L_1\) spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of \(L_1\) splines on 5-point windows.
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convexity
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cubic \(L_1\) spline
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5-point window
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interpolation
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linearity
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locally calculated
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oscillation
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second-derivative-based
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univariate
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