Univariate cubic L 1 interpolating splines based on the first derivative and on 5-point windows: analysis, algorithm and shape-preserving properties |
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Authors: | Qingwei Jin Lu Yu John E. Lavery Shu-Cherng Fang |
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Affiliation: | 1. Department of Management Science and Engineering, Zhejiang University, Hangzhou, China 2. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695-7906, USA 3. Mathematical Sciences Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC, 27709-2211, USA
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Abstract: | In this paper, univariate cubic L 1 interpolating splines based on the first derivative and on 5-point windows are introduced. Analytical results for minimizing the local spline functional on 5-point windows are presented and, based on these results, an efficient algorithm for calculating the spline coefficients is set up. It is shown that cubic L 1 splines based on the first derivative and on 5-point windows preserve linearity of the original data and avoid extraneous oscillation. Computational examples, including comparison with first-derivative-based cubic L 1 splines calculated by a primal affine algorithm and with second-derivative-based cubic L 1 splines, show the advantages of the first-derivative-based cubic L 1 splines calculated by the new algorithm. |
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