It is the cache of ${baseHref}. It is a snapshot of the page. The current page could have changed in the meantime.
Tip: To quickly find your search term on this page, press Ctrl+F or ⌘-F (Mac) and use the find bar.

Differentiation and Numerical Integral of the Cubic Spline Interpolation | Gao | Journal of Computers
Journal of Computers, Vol 6, No 10 (2011), 2037-2044, Oct 2011
doi:10.4304/jcp.6.10.2037-2044

Differentiation and Numerical Integral of the Cubic Spline Interpolation

Shang Gao, Zaiyue Zhang, Cungen Cao

Abstract


Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and unequally spaced data. The formulas based on cubic spline interpolation solving numerical integral of discrete function are deduced. The degree of integral formula is n=3.The formulas has high accuracy. At last, these calculation methods are illustrated through examples.


Keywords


cubic spline function; numerical differentiation, numerical integral; first derivative; second derivative

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


Journal of Computers (JCP, ISSN 1796-203X)

Copyright @ 2006-2014 by ACADEMY PUBLISHER – All rights reserved.