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Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows
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Algorithms 2010, 3(3), 311-328; doi:10.3390/a3030311

Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm

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: 11 July 2010 / Accepted: 10 August 2010 / Published: 20 August 2010
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
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Abstract

We compare univariate L1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than the other types of L1 splines. To calculate second-derivative-based 5-point-window L1 splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm.
Keywords: antiderivative; cubic L1 spline; first derivative; 5-point window; function value; global; interpolation; locally calculated; second derivative; univariate antiderivative; cubic L1 spline; first derivative; 5-point window; function value; global; interpolation; locally calculated; second derivative; 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

Yu, L.; Jin, Q.; Lavery, J.E.; Fang, S.-C. Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm. Algorithms 2010, 3, 311-328.

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