The Interval Rational- Interpolation Method

Fuzzy Optimization and Modeling Journal

مقاله 4، دوره 3، شماره 2، تیر 2022، صفحه 23-39   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/fomj.2022.1944092.1045

نویسندگان

Hajar Rasekhinezhad¹؛ Mozhdeh Afshar Kermani^{* 2}؛ Tofigh Allahviranloo³؛ Saeid Abbasbandy⁴؛ Esmail Babolian⁵

¹Department of mathematics, Science and research Branch, Islamic Azad University, Tehran, Iran

²Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

³Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey.

⁴Department of Applied Mathematics, Faculty of science, Imam Khomeini International University, Qazvin, Iran

⁵Department of Computer Science, Faculty of Mathematical Science and Computer, Kharazmi University, Tehran, Iran

چکیده

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.

کلیدواژه‌ها

Interval Value؛ Rational Interpolation؛ Interval Arithmetic؛ Rational Function