The Study Focuses on Lacunary Interpolation and Error Estimations by Spline Function
DOI:
https://doi.org/10.56714/bjrs.50.2.12Keywords:
Lacunary Interpolation, Spline Function, Error Bounds, Convergence AnalysisAbstract
To solve a lacunary interpolation problem with a range of (0, 2, 4), we first look at an appropriate class of insufficient splines. Under suitable assumptions, we prove the existence and uniqueness of the solution. We describe the convergence analysis and show that the approach is of order six and that it can be constructed of any order, with any intermediate lacunary requirements.
Downloads
References
R. G. Karem, K. H. F. Jwamer, and F. K. Hamasalh, "Lacunary interpolation by the spline function of fractional degree," Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 15, no. 3, pp. 54–72, 2023. DOI: 10.29304/jqcm.2023.15.3.1282.
K. H. Jwamer, "Study some of the lacunary interpolation by splines and their error bounds," M.Sc. Thesis, Salahaddin University, Erbil, Iraq, 2001.
K. H. Jwamer, "Minimizing error bounds in (0, 2, 3) lacunary interpolation by sixtic spline," American Journal of Mathematics and Statistics, vol. 3, no. 4, pp. 249–256, 2007.
R. G. Karem, K. H. F. Jwamer, and F. K. Hamasalh, "Existence, uniqueness, and stability results for fractional differential equations with lacunary interpolation by the spline method," Mathematics and Statistics, vol. 11, no. 4, pp. 669–675, 2023. DOI: 10.13189/ms.2023.110408.
F. K. Hamasalh and K. H. F. Jwamer, "On optimality of lacunary interpolation for recovery of C6C^6C6 seventh-degree spline," International Journal of Open Problems in Computer Mathematics, vol. 5, no. 1, Mar. 2012. DOI: 10.12816/0006097.
K. H.-F., F. K. H.-S., and R. K. G., "Approximation new error bounded by spline degree six," Acta Universitatis Apulensis, Special Issue, Romania, 2011.
K. H. Jwamer and F. K. Hama-Salh, "Minimizing error bounds in lacunary interpolation by spline (0, 2) case," Journal of Kirkuk University - Scientific Studies, vol. 4, no. 2, pp. 117–124, 2009.
S. R. K. and K. H. F. Jwamer, "Lacunary interpolation by spline function - (0, 1, 4) case," Journal of Dohuk University, vol. 4, no. 2, pp. 193–196, 2001. Available: ResearchGate.
G. M. Phillips, Interpolation and Approximation by Polynomials. New York: Springer Verlag, 2003.
R. K. Saeed and K. H. Jwamer, "Minimizing error bounds in lacunary interpolation by spline function (0, 1, 4) case," Journal of Al-Nahrain University, vol. 8, no. 2, pp. 114–119, 2005.
R. K. Saeed, "(0, 1, 3, 5) Lacunary interpolation by deficient splines," Journal of Science and Nature, vol. 2, no. 1, pp. 28–30, 1993. DOI: 10.12691/ajna-4-1-3.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Basrah Researches Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.