Deficient quartic spline of Marsden type with minimal deviation by the data polygon
DOI:
https://doi.org/10.24193/subbmath.2023.1.15Keywords:
Marsden type deficient quartic splines, optimal properties, minimal quadratic oscillation in averageAbstract
In this work we construct the deficient quartic spline with the knots following the Marsden's scheme and prove the existence and uniqueness of the deficient quartic spline with minimal deviation by the data polygon. The interpolation error estimate of the obtained quartic spline is given in terms of the modulus of continuity. A numerical example is included in order to illustrate the geometrical behaviour of the quartic spline with minimal quadratic oscillation in average in comparison with the two times continuous differentiable deficient quartic spline.
References
Ahlberg, J.H., Nilson, E.H., Walsh, J.L., The Theory of Splines and Their Applications, Academic Press, New York, London 1967.
Bica, A.M., Fitting data using optimal Hermite type cubic interpolating splines, Appl. Math. Lett., 25 (2012), 2047-2051.
Blaga, P., Micula, G., Natural spline functions of even degree, Studia Univ. Babes-Bolyai Cluj-Napoca Mathematica, 38 (1993), no. 2, 31-40.
Burmeister, W., Heß, W., Schmidt, J.W., Convex splines interpolants with minimal curvature, Computing, 35 (1985), 219-229.
Floater, M., On the deviation of a parametric cubic spline interpolant from its data polygon, Comput. Aided Geom. Des., 23 (2008),148-156.
Han, X., Guo, X., Cubic Hermite interpolation with minimal derivative oscillation, J. Comput. Appl. Math., 331 (2018), 82-87.
Howell, G., Varma, A.K., Best error bounds for quartic spline interpolation, J. Approx. Theory, 58 (1989), 58-67.
Kobza, J., Cubic splines with minimal norm, Appl. Math. 47 (2002), 285-295.
Kobza, J., Quartic splines with minimal norms, Acta Univ. Palacki. Olomuc, Fac. rer. nat., Mathematica, 40 (2001), 103-124.
Marsden, M., Quadratic spline interpolation, Bull. Amer. Math. Soc., 80 (1974), no. 5, 903-906.
Micula, Gh., Santi, E., Cimoroni, M.G., A class of even degree splines obtained through a minimum condition, Studia Univ. "Babeş-Bolyai" Mathematica 48 (2003), no. 3, 93-104.
Micula, G., Micula, S., Handbook of Splines, Mathematics and Its Applications, vol.462, Kluwer Academic Publishers, Dordrecht 1999.
Volkov, Yu. S., Best error bounds for the derivative of a quartic interpolation spline, Mat. Trud., 1 (1998), no. 2, 68-78 (in Russian).
Downloads
Additional Files
- Deficient quartic spline of Marsden type with minimal deviation by the data polygon
- Deficient quartic spline of Marsden type with minimal deviation by the data polygon
- Deficient quartic spline of Marsden type with minimal deviation by the data polygon
- Deficient quartic spline of Marsden type with minimal deviation by the data polygon
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.