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Neville’s Method of Polynomial Interpolation

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Neville’s method evaluates a polynomial that passes through a given set of and points for a particular value using the Newton polynomial form. Neville’s method is similar to a now-defunct procedure named Aitken’s algorithm and is based on the divided differences recursion relation (“Neville’s Algorithm”, n.d). It was stated before in a previous post on Lagrangian polynomial interpolation that there exists a Lagrange polynomial that passes through points where each is a distinct integer and at corresponding x values . The points are denoted . Neville’s Method Neville’s method can be stated as follows: Let a function be defined at points where and are two distinct members. For each , there exists a Lagrange polynomial that interpolates the function at the points . The th Lagrange polynomial is defined as: The and are often denoted and , respectively, for…
Original Post: Neville’s Method of Polynomial Interpolation