The Interval Rational- Interpolation Method

Subject Areas : Fuzzy Optimization and Modeling Journal

Hajar Rasekhinezhad ¹ (Department of mathematics, Science and research Branch, Islamic Azad University, Tehran, Iran)
Mozhdeh Afshar Kermani ² (Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran)
Tofigh Allahviranloo ³ (Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey.)
Saeid Abbasbandy ⁴ (Department of Applied Mathematics, Faculty of science, Imam Khomeini International University, Qazvin, Iran)
Esmail Babolian ⁵ (Department of Computer Science, Faculty of Mathematical Science and Computer, Kharazmi University, Tehran, Iran)

Received: 2021-11-06 Accepted : 2022-01-11 Published : 2022-04-01

Keywords: Interval value, Rational interpolation, Interval arithmetic, Rational function,

Abstract :

The rational interpolation sometimes gives better approximations than polynomial interpolation particularly for large sequence of points. In this paper, for the first time we provide a combination of rational interpolation and interval data. we present applied interval arithmetic in rational interpolation, when support points are interval-valued. First, we introduce the basic concepts of the algebraic theories to apply the interval methods to uncertainty analysis. Then the interpolation of interval coefficient is obtained and also the error of the proposed method is analyzed and is proved by a theorem for different cases. Some different numerical examples are given to illustrate the proposed method and the results are recorded.