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Adaptive B-spline knot selection using multi-resolution basis set

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  • Yuan Yuan
  • Nan Chen
  • Shiyu Zhou

Abstract

B-splines are commonly used to fit complicated functions in Computer Aided Design and signal processing because they are simple yet flexible. However, how to place the knots appropriately in B-spline curve fitting remains a difficult problems. This article discusses a two-stage knot placement method to place knots adapting to the curvature structures of unknown function. In the first stage, a subset of basis functions is selected from the pre-specified multi-resolution basis set using a statistical variable selection method: Lasso. In the second stage, a vector space that is spanned by the selected basis functions is constructed and a concise knot vector is identified that is sufficient to characterize the vector space to fit the unknown function. The effectiveness of the proposed method is demonstrated using numerical studies on multiple representative functions.

Suggested Citation

  • Yuan Yuan & Nan Chen & Shiyu Zhou, 2013. "Adaptive B-spline knot selection using multi-resolution basis set," IISE Transactions, Taylor & Francis Journals, vol. 45(12), pages 1263-1277.
    • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:12:p:1263-1277
    DOI: 10.1080/0740817X.2012.726758
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    Cited by:

    1. Gálvez, Akemi & Iglesias, Andrés, 2016. "Particle-based meta-model for continuous breakpoint optimization in smooth local-support curve fitting," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 195-212.
    2. Kovács, Péter & Fekete, Andrea M., 2019. "Nonlinear least-squares spline fitting with variable knots," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 490-501.

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