Univariate cubic L1 interpolating splines based on the first derivative and on 5-point windows: analysis, algorithm and shape-preserving properties

Authors:
Qingwei Jin;Lu Yu;John E. Lavery;Shu-Cherng Fang
Affiliations:
Department of Management Science and Engineering, Zhejiang University, Hangzhou, China and Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleig ...;Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA 27695-7906;Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA 27695-7906 and Mathematical Sciences Division, Army Research Office, Army Research L ...;Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA 27695-7906
Venue:
Computational Optimization and Applications
Year:
2012

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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.