Smoothing by spline functions

@article{Reinsch1967SmoothingBS,
  title={Smoothing by spline functions},
  author={Christian H. Reinsch},
  journal={Numerische Mathematik},
  year={1967},
  volume={10},
  pages={177-183}
}
  • C. Reinsch
  • Published 1 October 1967
  • Mathematics
  • Numerische Mathematik
In this paper we generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence. 
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A theorem that characterizes spline functions that both smooth and interpolate is given. A bivariate generalization is presented which permits interpolation and smoothing of informa- tion which is
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References

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On Pólya frequency functions IV: The fundamental spline functions and their limits
The present paper was written in 1945 and completed by 1947 (see the abstract [3]) but for no good reason has so far not been published. It appears now in a somewhat revised and improved form.
A general method for the construction of interpolating or smoothing spline-functions
Abstract : The spline interpolation problem was generalized by Atteia to an abstract minimization problem in a Hilbert space setting. In this paper, new and efficient derivations of the general
SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION.
  • I. J. Schoenberg
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1964
TLDR
The aim of this note is to extend some of the recent work on spline interpolation so as to include also a solution of the problem of graduation of data and the qualitative aspects of the new method are described.