Concepedia

Fifty years of Schoenberg’s problem on the convergence of spline interpolation

Yu. S. Volkov, Yu. N. Subbotin

Proceedings of the Steklov Institute of Mathematics · 2015 · 35 citations · 41 references

DOI

Concepts

Abstract

A review of results on the convergence of the interpolation process for polynomial splines and derivatives in the last 50 years is given.

References

41

Spline Functions: Basic Theory.

Philip W. Smith, Larry L. Schumaker · Mathematics of Computation · 1982 · 2.5K citations

, , +17

Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae

I. J. Schoenberg · Quarterly of Applied Mathematics · 1946 · 938 citations · Full text

, , +9

Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae

I. J. Schoenberg · Quarterly of Applied Mathematics · 1946 · 487 citations · Full text

, , +6

Optimal error bounds for cubic spline interpolation

Charles A. Hall, W. Weston Meyer · Journal of Approximation Theory · 1976 · 282 citations

, , +14

On error bounds for spline interpolation

Charles A. Hall · Journal of Approximation Theory · 1968 · 278 citations

, , +14