American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
American Journal of Applied Mathematics and Statistics. 2014, 2(3), 88-91
DOI: 10.12691/ajams-2-3-1
Open AccessArticle

Unique Lacunary interpolations with Estimate Errors Bound

Faraidun K. HamaSalh1, and Shko A. Tahir2,

1Department of Mathematics, School of Science Education, University of Sulaimani Iraq

2University of Sulaimani-Faculty of Science and Science Education School ofScience-Department of Mathematics, Sulaimani, Iraq

Pub. Date: March 31, 2014

Cite this paper:
Faraidun K. HamaSalh and Shko A. Tahir. Unique Lacunary interpolations with Estimate Errors Bound. American Journal of Applied Mathematics and Statistics. 2014; 2(3):88-91. doi: 10.12691/ajams-2-3-1


This paper presents a formulation of a Lacunary approximation for the class ninth of spline function at uniform mesh points and the function values at the end points of the interval. Error bounds for the function and its derivatives are derived. Finally, efficiency estimation and convergence orders are also illustrate errors derivations.

lacunary interpolations function convergence analysis differential equations

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Faraidun K. Hama-Salh, Karwan H. F. Jwamer, Cauchy problem and Modified Lacunary Interpolations for Solving Initial Value Problems, Int. J. Open Problems Comp. Math., Vol. 4, No. 1, pp. 172-183, 2011.
[2]  Gyovari, J., Cauchy problem and Modified Lacunary Spline functions, Constructive Theory of Functions.Vol.84, pp. 392-396, 1984.
[3]  Kendall Atkinson, Weimin Han, Theoretical Numerical Analysis, A Functional Analysis Framework, Third Edition, 2009.
[4]  Klaus Ritter, Average-Case Analysis of Numerical Problems, Springer-Verlag Berlin Heidelberg New York, 2000.
[5]  Lyman M. Kells, Elementary Differential Equations. Sixth Edition, (1960).
[6]  Rana, S. S. and Dubey, Y. P., Best error bounds for deficient quartic spline interpolation, Indian J. Pure Appl. Math., 30 (4), 385-393, 1999.
[7]  Richard L. Burden, J. Douglas Faires, Numerical Analysis, 9th Edition, Brooks/Cole, Cengage Learning, 2011.
[8]  Rostam K. Saeed, Faraidun K. Hamasalh and Gulnar W. Sadiq, Convergence of Ninth Spline Function to the Solution of a System of Initial Value Problems, World Applied Sciences Journal 16(10):1360-1367, 2012.
[9]  Saxena, A., Solution of Cauchy's problem by deficient lacunary spline interpolations, Studia Univ. BABES-BOLYAI MATHEMATICA, Vol. XXXII, No.2, 60-70, 1987.