Email this article On a Generalization of Cubic Spline Interpolation
Abstract
Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arbitrary two nodes or second derivatives of arbitrary two node are given. At last, these calculation methods are illustrated through examples.
Keywords
References
[1] P. Sablonnière. Gradient approximation on uniform meshes by finite differences and cubic spline interpolation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v 5654 LNCS, p 322-334, 2009.
[2] J. S. Behar, S. J. Estrada, M. V. Hernández. Constrained interpolation with implicit plane cubic a-splines. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v 5197 LNCS, p 724-732, 2008.
[3] Petrinovic, Davor. Causal cubic splines: Formulations, interpolation properties and implementations. IEEE Transactions on Signal Processing, v 56, n 11, p 5442-5453, 2008.
http://dx.doi.org/10.1109/TSP.2008.929133
[4] R. L. Burden, J.D. Faires. Numerical Analysis. Higher Education Press & Thomson Learning, Inc., 2001,pp.141-150, 408-409.
[5] J. H. Mathews, K.D. Fink. Numerical Methods Using MATLAB. Publishing House of Electronics Industry, 2002, pp.280-290.
[6] M. I. Syam. Cubic spline interpolation predictors over implicitly defined curves. Journal of Computational and Applied Mathematics, 2003, 157(2), pp.283-295.
http://dx.doi.org/10.1016/S0377-0427(03)00411-4
[7] T. L. Tsai, I. Y. Chen. Investigation of effect of endpoint constraint on time-line cubic spline interpolation. Journal of Mechanics, v 25, n 2, p 151-160, June 2009.
http://dx.doi.org/10.1017/S1727719100002604
Full Text: PDF