Numerische Mathematik

, Volume 42, Issue 1, pp 107–117

Natural spline functions, their associated eigenvalue problem

  • Florencio Utreras

DOI: 10.1007/BF01400921

Cite this article as:
Utreras, F. Numer. Math. (1983) 42: 107. doi:10.1007/BF01400921


We consider the problem of studying the behaviour of the eigenvalues associated with spline functions with equally spaced knots. We show that they are\(O\left( {\frac{{i^{2m} }}{n}} \right)i = 1, \ldots ,n - m\) wherem is the order of the spline andn, the number of knots.

This result is of particular interest to prove optimality properties of the Generalized Cross-Validation Method and had been conjectured by Craven and Wahba in a recent paper.

Subject Classifications

AMS(MOS): 65D05CR: 5.13

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Florencio Utreras
    • 1
  1. 1.Departamento de Matematicas, Facultad de Ciencias Fisicas y MatematicasUniversidad de ChileSantiagoChile