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Algorithms 2010, 3(3), 276-293; doi:10.3390/a3030276

Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows

1
Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, USA
2
Mathematical Sciences Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211, USA
*
Author to whom correspondence should be addressed.
Received: 9 June 2010 / Revised: 11 July 2010 / Accepted: 20 July 2010 / Published: 30 July 2010
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
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Abstract

We analytically investigate univariate C1 continuous cubic L1 interpolating splines calculated by minimizing an L1 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 L1 spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of L1 splines on 5-point windows.
Keywords: convexity; cubic L1 spline; 5-point window; interpolation; linearity; locally calculated; oscillation; second-derivative-based; univariate convexity; cubic L1 spline; 5-point window; interpolation; linearity; locally calculated; oscillation; second-derivative-based; univariate
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Jin, Q.; Lavery, J.E.; Fang, S.-C. Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows. Algorithms 2010, 3, 276-293.

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