A class of cubic splines obtained through minimum conditions

Bini, D.; Capovani, M.

doi:10.1090/S0025-5718-1986-0815840-5

A class of cubic splines obtained through minimum conditions
HTML articles powered by AMS MathViewer

by D. Bini and M. Capovani PDF

Math. Comp. 46 (1986), 191-202 Request permission

Abstract:

A class of cubic spline minimizing some special functional is investigated. This class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter $\alpha < 2$. For $\alpha = 1/2$ natural splines are obtained. For $\alpha = - 1$ the spline minimizing the mean value of the third derivative is obtained. It is shown that this spline has the best convergence order.

References

J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The theory of splines and their applications, Academic Press, New York-London, 1967. MR 0239327
Dario Bini and Milvio Capovani, Spectral and computational properties of band symmetric Toeplitz matrices, Linear Algebra Appl. 52/53 (1983), 99–126. MR 709346, DOI 10.1016/0024-3795(83)80009-3
A. Ghizzetti, Interpolation with splines satisfying a suitable condition, Calcolo 20 (1983), no. 1, 53–65 (Italian, with English summary). MR 747007, DOI 10.1007/BF02575892
D. Kershaw, A note on the convergence of interpolatory cubic splines, SIAM J. Numer. Anal. 8 (1971), 67–74. MR 281318, DOI 10.1137/0708009
J. Stoer and R. Bulirsch, Introduction to numerical analysis, Springer-Verlag, New York-Heidelberg, 1980. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. MR 557543