An extension of Lagrange interpolation formula and its applications

Document Type : Original Article

Authors

1 Financial Mathematics Department, Finance Faculty, Kharazmi University, Tehran, Iran

2 Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

Abstract

In this work, a new type of interpolation formula is introduced. These formulas can be an extension of the Lagrange interpolation formula. The error of this new type of interpolation is calculated. In order to display efficiency of the proposed formulas, three numerical examples are presented.

Keywords

Main Subjects


[1] W. Cheney, W. Light, A course in approximation theory, Books/Cole Publishing Company, 2000.
[2] C. Disibüyük, A functional generalization of the interpolation problem, Applied Mathematics and Computation, 256 2015, 247-251.
[3] M.A. Jafari, A. Aminataei, Some applications of Sigmoid functions, Iranian Journal of Numerical Analysis and Optimization, 11(1) (2021), 221-233.
[4] M.A. Jafari, A. Aminataei, Some new kinds of interpolation formulas and its applications, Mathematics and Computational Sciences, 3(3) 2022, 40-46.
[5] M. Masjed-Jamei, G.V. Milovanovic, Z. Moalemi, A generalization of divided differences and applications, Filomat, 33 2019, 193-210.
[6] M. Masjed-Jamei, Z. Moalemi, W. Koepf, A unified representation for some interpolation formulas, Analysis, 40 2020, 113-125.
[7] G. Mastroianni, G. V. Milovanovi´ c, Interpolation processes: Basic theory and applications, Springer, 2008.
[8] J. Stoer, R. Bullirsch, Introduction to Numerical Analysis, Springer, 2002.