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Computational Optimization and Applications

, Volume 51, Issue 2, pp 575–600 | Cite as

Univariate cubic L 1 interpolating splines based on the first derivative and on 5-point windows: analysis, algorithm and shape-preserving properties

  • Qingwei JinEmail author
  • Lu Yu
  • John E. Lavery
  • Shu-Cherng Fang
Article

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.

Keywords

Cubic L1 spline First-derivative-based Interpolation Locally calculated Shape preservation 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Qingwei Jin
    • 1
    • 2
    Email author
  • Lu Yu
    • 2
  • John E. Lavery
    • 2
    • 3
  • Shu-Cherng Fang
    • 2
  1. 1.Department of Management Science and EngineeringZhejiang UniversityHangzhouChina
  2. 2.Edward P. Fitts Department of Industrial and Systems EngineeringNorth Carolina State UniversityRaleighUSA
  3. 3.Mathematical Sciences Division, Army Research OfficeArmy Research LaboratoryResearch Triangle ParkUSA

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