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The use of the stochastic arithmetic to estimate the value of interpolation polynomial with optimal degree |
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| Authors: | S Abbasbandy M A Fariborzi Araghi |
| Institution: | a Department of Mathematics, Imam Khomeini International University, PO Box 288, Gazvin 34194, Iran b Department of Mathematics, Islamic Azad University, Tehran Branch, Tehran, Iran |
| Abstract: | One of the considerable discussions in data interpolation is to find the optimal number of data which minimizes the error of the interpolation polynomial. In this paper, first the theorems corresponding to the equidistant nodes and the roots of the Chebyshev polynomials are proved in order to estimate the accuracy of the interpolation polynomial, when the number of data increases. Based on these theorems, then we show that by using a perturbation method based on the CESTAC method, it is possible to find the optimal degree of the interpolation polynomial. The results of numerical experiments are presented. |
| Keywords: | Interpolation polynomial Chebyshev polynomial Stochastic arithmetic CESTAC method |
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