General Mathematics, Vol. 10,nr. 1-2, 2002
Abstract:
Spline functions have proved to be very useful in numerical analysis, in numerical treatment of differential, integral and partial differential equations, in statistics, and have found applications in science, engineering, economics, biology, medicine, etc. It is well known that interpolating polynomial splines can be derived as the solution of certain variational problems. This paper presents a variational approach to spline interpolation. By considering quite general variational problems in abstract Hilbert spaces setting, we derive the concept of "splines". The aim of this paper is to present a sequence of theorems and results starting with Holladay's classical results concerning the variational property of natural cubic splines and culminating in some general variational approach in abstract splines results.
Full text of the article: