A class of cubic splines obtained through minimum conditions
Authors: D. Bini and M. Capovani
Journal: Math. Comp. 46 (1986), 191-202
MSC: Primary 41A15; Secondary 65D07
MathSciNet review: 815840
Full-text PDF Free Access
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.
- 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 https://doi.org/10.1016/0024-3795%2883%2980009-3
- A. Ghizzetti, Interpolation with splines satisfying a suitable condition, Calcolo 20 (1983), no. 1, 53–65 (Italian, with English summary). MR 747007, DOI https://doi.org/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 https://doi.org/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
J. H. Ahlberg, E. N. Nilson & J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York, 1967.
D. Bini & M. Capovani, "Spectral and computational properties of band symmetric Toeplitz matrices," Linear Algebra Appl., v. 52/53, 1983, pp. 99-126.
A. Ghizzetti, "Interpolazione con splines verificanti una opportuna condizione," Calcolo, v. 20, 1983, pp. 53-65.
D. Kershaw, "A note on the convergence of interpolatory cubic splines," SIAM J. Numer. Anal., v. 8, 1971, pp. 67-74.
J. Stoer & R. Bulirsch, Introduction to Numerical Analysis, Springer, Berlin, 1980.