Applied Mathematics & Information Sciences

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Interpolation formula is an important concept in the theory of numerical analysis which is grown up based on interpolation. So, to study the interpolation in interval environment, interval interpolation formulae are more essential. The objective of this article is to establish extended Newton’s interpolation formulae for interval-valued functions using p- difference of intervals. For this purpose, parametric representation of intervals with interval arithmetic in the parametric form and parametric representation of interval-valued function have been discussed briefly. Using p-difference of intervals, finite differences (forward/backward) of interval-valued function have been defined and called them as Newton’s p-difference (forward/backward) operators. After that fundamental theorem of finite difference calculus has been extended for polynomials with interval-valued coefficients. Then Newton’s p-difference interpolation formulae (forward/backward) have been derived. Also, computational algorithm for forward p-difference interpolation has been established. Finally, with the help of graphical representation of a numerical example, it has been shown that both the p-difference interpolation formulae (forward and backward) are identical. It should be noted that the proposed interpolation formulae are the generalization of traditional Newton’s interpolation formulae (forward and backward).

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