Abstract
The quartic spline of interpolation generated by initial conditions is constructed. The initial values corresponding to the first, second and third derivative of spline in the first knot are uniquely determined such that the quadratic oscillation in average of the quartic spline to be minimal (this notion was recently introduced by the author for any spline of interpolation function).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahlberg, J.H., Nilson, E.N., Walsh, J.L.: The theory of splines and their applications. Academic Press, New York (1967)
Bica, A.M.: Iterative numerical methods for operatorial equations. University of Oradea Press (2006)
Bica, A.M., Căuş, V.A., Fechete, I., Mureşan, S.: Application of the Cauchy-Buniakovski-Schwarz’s inequality to an optimal property for cubic splines. J. of Computational Analysis and Applications 9(1), 43–53 (2007)
De Boor, C.: A practical guide to splines. Applied Math. Sciences, vol. 27. Springer, Berlin (1978)
Gao, X., Shu, S., Fu, K.: Quartic spline on spline interpolation. J. Comput. Appl. Math. 71(2), 213–223 (1996)
Grandine, T.A., Hogan, T.A.: A parametric quartic spline interpolant to position, tangent and curvature. Computing 72(1-2), 65–78 (2004)
Howell, G., Varma, A.K.: Best error bounds for quartic spline interpolation. J. Approximation Theory 58(1), 58–67 (1989)
Iancu, C.: On the cubic spline of interpolation. Semin. of Funct. Anal. and Num. Meth. 4, 52–71 (1981) (preprint)
Karaballi, A.A., Sallam, S.: Quartic spline interpolation on uniform meshes with application to quadratures. J. Math. Res. Expo. 19(3), 533–538 (1999)
Micula, G., Micula, S.: Handbook of splines. Mathematics and its Applications, vol. 462. Kluwer Academic Publishers, Dordrecht (1999)
Rana, S.S., Dubey, Y.P.: Best error bounds for deficient quartic spline interpolation. Indian J. Pure Appl. Math. 30(4), 385–393 (1999)
Rana, S.S., Gupta, R.: Deficient discrete quartic spline interpolation. Rocky Mt. J. Math. 35(4), 1369–1379 (2005)
Usmani, R.A.: Error bounds in periodic quartic spline interpolation. Approx. Theory Appl. 12(3), 1–9 (1996)
Usmani, R.A.: On nonperiodic quartic spline interpolation. Int. J. Comput. Math. 57(3-4), 197–211 (1995)
Volkov, Y.S.: Best error bounds for the derivative of a quartic interpolation spline. Sib. Adv. Math. 9(2), 140–150 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bica, A.M. (2009). Quartic Spline of Interpolation with Minimal Quadratic Oscillation. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-00464-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
Online ISBN: 978-3-642-00464-3
eBook Packages: Computer ScienceComputer Science (R0)