# 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} }

In this paper we generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence.

## 2,148 Citations

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## References

SHOWING 1-5 OF 5 REFERENCES

On Pólya frequency functions IV: The fundamental spline functions and their limits

- Mathematics
- 1966

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

- Mathematics
- 1968

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.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1964

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.