The use of the stochastic arithmetic to estimate the value of interpolation polynomial with optimal degree

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 estima...

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Bibliographic Details
Published in:Applied numerical mathematics 2004-09, Vol.50 (3), p.279-290
Main Authors: Abbasbandy, S, Fariborzi Araghi, M.A
Format: Article
Language:English
Subjects:
Approximations and expansions
CESTAC method
Chebyshev polynomial
Exact sciences and technology
Interpolation polynomial
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Stochastic arithmetic
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Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2004.01.003