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• Lavery, J
• Fang, S
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• Lavery, J
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Algorithms 2010, 3(3), 276-293; doi:10.3390/a3030276

Article

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

Qingwei Jin ^1,* , John E. Lavery ^1,2  and Shu-Cherng Fang ¹

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; in revised form: 11 July 2010 / Accepted: 20 July 2010 / Published: 30 July 2010

(This article belongs to the Special Issue Algorithms for Applied Mathematics)

Download PDF Full-Text [150 KB, uploaded 30 July 2010 14:44 CEST]

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

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