Interpolation Definition/Meaning:

A simple means of approximating a function ƒ(x) in which the approximation, say p(x), is constructed by requiring that

p(x_i) = ƒ(x_i) i = 0,1,2,...n

Here ƒ(x_i) are given values p(x_i) that fit exactly at the distinct points x_i (compare smoothing). The value can ƒ be approximated by p(x) for x ≠ x_i.

In practice p is often a polynomial, linear and quadratic polynomials providing the simplest examples. The process is also widely used in the construction of many numerical methods, for example in numerical integration. In addition the idea can be extended to include matching of p'(x_i) with ƒ'(x_i) ; this is Hermite interpolation.

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