Constrained smoothing of noisy data using splines in tension

Research output: Contribution to journalArticle (Academic Journal)peer-review

20 Citations (Scopus)


A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers. The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example applications to synthetic data and a record of magnetic inclination from Hawaii are given.

Original languageEnglish
Pages (from-to)419-434
Number of pages16
JournalMathematical Geology
Issue number4
Publication statusPublished - May 2007


  • data analysis
  • curve fitting
  • Lagrange multipliers


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