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Interpolation is a mathematical method for constructing a function from a discrete set of data points. The interpolation function, or interpolant, should exactly coincide with the given data points, and it can also be evaluated for other intermediate input values within the sampled range. There are many applications of interpolation: A typical use-case that provides an intuitive picture is the plotting of a smooth curve through a given set of data points. Another use-case is to approximate complicated functions, which, for example, could be computationally demanding to evaluate. In that case, it can be beneficial to evaluate the original function only at a limited number of points, and use interpolation to approximate the function when evaluating it for intermediary points.
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If the requested polynomial degree of the interpolant is smaller than the number of data points minus one, then a least square fit is computed rather than an exact interpolation.
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